1. Communicate your expectations with the players out of game

You and your players seem to have different expectations for how their character sheet should influence their roleplay. To you, it's immersion-breaking when a character acts differently than what their ability score suggests. To others, ability scores are just numbers that define mechanics and statistical outcomes, and don't directly restrict roleplay style.

It would benefit your campaign if you held an out-of-game discussion to directly address your roleplaying expectations and concerns. Discuss how you think characters should behave if their Intelligence, Wisdom, or Charisma is notably high or low. Get feedback. Make sure your players' preferences are in sync with yours.

Note that it may be an uphill battle if your players disagree. While a PC's ability scores affect what tasks they can do and their likelihood of success, they don't dictate roleplay or how the player should act out the character's thoughts and choices. Strictly speaking, it's the player's choice whether or not the PC's mental ability scores affect their roleplay, and to what degree. Assuming they wrote the character, they probably know best how the character would act and behave.

2. Use checks when players roleplay differently from their ability scores

If you want the ability scores to matter more, then include more dice-based challenges. This is where you have the system mechanics on your side. Characters with low WIS are less likely to succeed an WIS-demanding task. You can also prompt players to make checks, and then you can intervene regarding their character based on their success or failure on the check.

For example, if a player forgets or misses a clue but their character has high INT, have them make an INT check. On a success, they get a reminder or hint from the GM.

These checks can also be used (albeit sparingly) when players roleplay above their PC's capabilities. If the low-CHA character delivers an eloquent speech, ask them to make a CHA check or related skill. On a failure, you narrate that the audience wasn't particularly moved.

When intervening this way, make sure to use the “Yes, and” style of narration. Yes, the high-WIS druid walks toward the spider cave, and then has a flash of insight and realizes it's a bad idea. Yes, the low-CHA barbarian tries to speak politely and articulately, and the duke dislikes their untidy appearance and finds the speech unsettling. This way you still respect player agency, while maintaining narrative flow and nudging them to act more in-character.

3. Give in-game rewards for good roleplaying

Another way to encourage players is to give in-game incentives. Avoid big rewards like bonus XP, because that can seem unfair and subjective; from my experience, GMs who give roleplaying XP may seem biased toward certain players, which quickly results in player frustration.
Also avoid punishing players for what you consider bad roleplaying. Accusing players of bad roleplay when they are putting effort into roleplay could discourage them from roleplaying at all.

Instead, reward players for roleplaying in character and maintaining immersion. Use small rewards, like a temporary circumstance bonus for roleplaying in accordance with the ability score. This could encourage players to roleplay having low stats. They're already disadvantaged mechanically, and a temporary bonus would increase their odds of success.

Let's see what the rules have to say on this issue:

Metagaming: This is when characters act on information
that they don’t have access to, but which their players know
from the real world. Metagaming comes into play when
players fail to maintain a divide between in-character
knowledge and out-of-character knowledge. That could
include anything from uncannily accurate in-character
predictions from a player who’s already read the adventure,
players recognizing monsters when their characters
wouldn’t, low-Intelligence characters accessing well educated players’ knowledge and talents, etc. (Pathfinder RPG GameMastery Guide p.9)

One particularly sticky area of metagaming has
nothing to do with game mechanics, but rather real-world knowledge and intelligence. Sometimes the player
who’s a genius at solving puzzles and riddles wants to
play a dumb brute of a swordsman. This is great—so long
as his character isn’t still solving all the puzzles. In this
situation (or the reverse, where the player who’s terrible at
puzzles has an Intelligence score of 22), let all the players
work together to solve the puzzle, but use skill checks
and Intelligence checks to offer hints or determine who
actually comes up with the solution. Similarly, don’t fall
into the trap of letting a player’s knowledge base inform
the character’s beyond what’s reasonable. Just because
your player knows how to make gunpowder out of bat
guano doesn’t mean his uneducated halfling cleric does. (Pathfinder RPG GameMastery Guide p.9)

Though the above quotes are under the topic of metagaming, they clearly show to what degree that ability scores matter when role-playing a character.

James Jacobs (Paizo Creative Director) advises (in support of the rules stated above) on the Paizo forums

It's easier for the GM to play a high Int NPC, since he can use metagame info to fake the high intellect. For a PC, I sometimes do the same, but I also tend to put a few extra skill points in knowledge skills to help set up the fact that my character's a smartie. I also try to use more metagame knowledge as well, subject to GM approval. Patrick plays a super smart wizard in one of my games, and he plays his character as slightly mad—other folks are just to stupid to understand the reasons he does what he does. He sometimes laces made-up words into his character's dialogue and then defines them for the other players, simulating a larger vocabulary than other characters (and other players).

Low mental ability scores generally indicate some sort of madness or brain damage or personality flaw.

Low INT: Play the character by making dumb choices or having trouble reading or the like. Avoid putting ANY ranks into Int-based skills.

Low WIS: Play the character as super impulsive, little common sense, and kind of oblivious to things. Get distracted a lot.

Low CHA: Play the character as a jerk, or alternately as someone who just doesn't have much personality at all. A character who simply doesn't say much or hangs back during non-combat encounters. Frankly... this type of character, the one who avoids actual roleplaying or is antagonistic, is my LEAST favorite type of character to play, so my characters tend to always have above average Charisma scores if possible.

Since you are playing Pathfinder, explain to the player that in the Pathfinder rules, ability scores are directly tied to how you play your character. In addition to the Pathfinder RPG GameMastery Guide quotes above, have him read the Ability scores section of the Core Rulebook (p.15-17). This page has the same information, except where noted. Ability scores inform the player where the character stands in the game world. Let's take a look at their descriptions.

Strength (Str): Strength measures muscle and physical power.

Dexterity (Dex): Dexterity measures agility, reflexes, and balance.

Constitution (Con): Constitution represents your character’s health and stamina.

Intelligence (Int): Intelligence determines how well your character learns and reasons.

Wisdom (Wis): Wisdom describes a character’s willpower, common sense, awareness, and intuition.

Charisma (Cha): Charisma measures a character’s personality, personal magnetism, ability to lead, and appearance.

Why is it important to try to role-play according to your character's ability scores, besides it being an integral part of the rules? The 3.5 Dungeon Master's Guide helps with this stating:

The most important purpose of a campaign is to make the players feel that their characters live in a real world. This appearance of realism, also called verisimilitude, is important because it allows the players to stop feeling like they’re playing a game and start feeling more like they’re playing roles. (DMG 3.5 p.129)

The rules for ability scores are meant to help facilitate this very thing. Just as numbers help us make sense of reality, they also help us make sense of a fantasy world.

As an example, lets pit a human with a Strength of 20 vs a human with a strength 5. By the rules the character with the Strength of 20 can lift 400 pounds over his head. The character with a Strength of 5 can only lift a 100 pounds over his head. No matter how a player wants to role-play, this is a fact.

I once had a player, that played a character with a Wisdom of 20 extremely impulsive and rushed into deadly situations. After a few times of asking if he really wanted to do such things (to which he replied "Yes"). I asked him did he really think a character with a Wisdom of 20 would do these things? He said, "No, it's kinda the opposite of being wise, huh?". Afterwards, he started playing the character in a wiser fashion, and he was happy. When a character has a high Intelligence, Wisdom, or both, I let the group put their heads together (if they want to) to help make the character's choices more believable (like what the GameMastery Guide states above).

I shared all the above with one of my groups Saturday night. The result...it helped each member become more involved in the role-play of their characters. Yes!

Obviously a player is still free to play how he wants. Let him know that if he plays his 5 intelligence character to smart he's metagaming, and explain why it's harmful to the game (i.e. it disparages belief in the fantasy world you've created).

Does this mean that a 5 intelligence character can never have a good idea, obviously not. Have him roll intelligence checks. If he's succeeds at a notable amount, which is doubtful, he can keep up the ruse a bit longer. He could also make bluff checks to appear more intelligent than he really is.

If he's playing with high scores as if they're low (e.g. a wizard with a 20 intelligence playing as if it was 5) have him make bluff checks as he is trying to hide his true intellect or clarify if his character is insane.

The Pathfinder rules are on your side, but it takes players and a GM to play. Most players will cut the GM some slack if he can give good reasons for his decisions, seeing as he does most of the work.

The only way to encourage people to roleplay their character's stats as opposed to their own player stats, is simply that:

Encourage.

You can also directly ask, but expect each player to have a different definition as to what that actually means.

It is part of the invisible and (usually) unwritten social contract that any group of people who gather together to play a game form. There is an assumption that people are going to play by the rules, and that everyone has an understanding of the rules. There is an expectation that no one is going to be a jerk, or cheat. Note that assumptions and expectations are different, and violating either will result in different reactions from the people in question.

As these agreements are social constructions, the only means of "enforcing" them is also social in nature: peer pressure, discussion, argument, and so forth. Also, having a mindset of "enforcing" is perhaps not the best approach to a fun and enjoyable game, unless everyone in the group are rules fanatics of some type or another.

If people do not wish to play characters whose stats are at the mercy of the dice (I personally know one player who detests this, and refuses to play any character in d20 or D&D who has even a single stat lower than 12,) then you either use the alternate point buy system from the rules, or you enter the homebrew zone.

This is not necessarily a bad thing, however, most DMs have a difficult enough time running the game as written, let alone when bits and pieces of it are edited on the fly without extensive testing. So it is a case of being aware of how changes will affect gameplay, and enjoyment of the game.

Since D&D (which is Pathfinder's direct ancestor) itself is a homebrew version of Chainmail, you'll be in fine tradition as you modify the game to suit your group.

Your best approach is to make it a group discussion and find a balance that suits your group, write it down for reference (it's always wise to write down on the cuff decisions, homebrew modifications, and group decisions for future reference), and have fun.

Your players will have more fun if you don't do this.

Remember that D&D is a game for the players, and that means the players should get to make interesting decisions.

It's not fun if the group asks you to never do anything clever because your character has a low intelligence. It's also not fun if you have to get collective buy-in on all your decisions because the DM has told you you're not playing your character as smart enough by yourself. (You've told us that you said that to someone and they didn't take it as an insult. I think many people would take it as an insult.)

The game already includes mechanical consequences for having low mental stats: you get penalties to noticing things, to remembering things, and to persuading people of things. You've noted the consequences are pretty small, and that's by design.

If you wanted to have worse consequences for having low mental stats, the right way to do that would be to increase the bonuses and penalties for mental stats: maybe your diplomacy rolls use double or triple your CHA modifier, or something like that.

I don't recommend it, though. Your players will have more fun if nobody is "too incompetent" to attempt certain skill checks.

Ability scores inform roleplaying styles, rather than dictating it.

As Mike Q's answer covered, what ability scores can do dictate is any mechanical skill checks. If you can't convince the players to RP according to their stats, then you can influence the RP flow using skill checks.

Well, first ask the key question: is everyone having fun? Could they have more fun? If people find this stat-are-irrelevant RP game style more fun, don't muck it up!

If someone is playing their character as though they have more skill, let them. Let them tie their own noose. Let them BS their way into a situation where they actually have to make a roll on that skill or stat. Have that roll have actual lasting consequences. If the Cha -2 tries to con the Innkeeper's daughter into spending the night with him, let him RP the scene. At some point, a roll takes place. The result of that role just might affect whether your party is welcome to stay at that Inn in the future. Or even stay in the town, depending on how close knit they all are!

If your character with a poor intimidate roll tries to intimidate his way into the palace, let him try. Have the outer guards play nice. Its the inner guards who will call for a roll, after you have no more escape routes!

Sandbagging

If someone is sandbagging, that can be more tough. There are not many situations where you want to fail at something, so a wizard that is sandbagging their high int scores is hard to fix.

But nobody likes a sandbagger. Get your party into a situation where the wizard needs to do something that is intelligence based publicly. Let the town see how smart he is. Then the town can start holding him to his intellect, acting disappointed in him if he doesn't measure up. Perhaps the key person they need to talk to in order to move their quest forward seems saddened to see the party hanging out with this loser. A new RP situation begins around how they keep the wizard included despite this NPC's prejudice.

In all cases, the RP goes as the player wants it to go. But at some point, rubber meets the road. That's where the skill checks come. Make them meaningful.