Overpair vs Regular, drawy board 3bet pot.

Preflop, I would've played the same.

The flop I would have check/called. This player doesn't fold to Cbets on the flop that often and you have no draw. When villain checks on the turn, you can choose to bet and take the pot because he doesn't go to showdown that often (35%). If he raises you, you are behind anyway but you will have then more complete info of your situation.

To exploit people you sometimes need to play exploitable

You cannot x/call flop as we are IP.
We can cbet as villain will call with a wide range of 1club hands, Qx, even Jx.

You could check back the flop and to bluffcatch him on turn and river if he decides to bluff some A♣:. Villains range is not that wide. You can't continue with your hand if you get raised and villain is going to raise you often with A♣: hands.

You must x back OTF. This board hits UTG range very hard, he is nitty, he's calling range pre is something like QQ/JJ/AK and maybe some AQs/KQs. On blank turn c if UTG bets and bet yourself 2/3 if he x.

Totally agree with LuckManFromLT, this is a check back on the flop. You need to keep villains ranges wide, which is what you are NOT doing by betting half pot here vs nitty opponent you are narrowing down vs value range only which your overpair is not doing so great against. Think about it, if you know that villain folds all hands that you beat to your Cbet BUT stays in the hand with hands that beat yours, then the expected value of your bet itself is never positive. So strengthen your own checkback range here, if he flopped a flush like <1% of the time well so be it gg, however, I do also think that sets are a good part of his range here or perhaps top pair with NFD (even though less likely because you are already holding 2 Aces and AQ offsuit is not just that likely here anyway). So proceed with caution.

I don't like checking back the flop and giving him a free chance to hit a flush with 1 card flushdraw. I also don't think we will be behind his continuing range. He will call with quite of worse hands, especially if he has a club. If he folds a flushdraw, fine by me. Better he folds than we check back and he hits. If he raises our cbet, I would fold. Maybe he would bluff with a flushdraw, indeed, but I don't expect this player to check/raise his draws.

With 12% OREP and 63% FT3B, we expect him to continue pre-flop with only the top 4.4% of hands, but we expect a 4-bet with KK+, so I agree with LuckyManFromLT that his pre-flop range is something like {AK, AQs, QQ, JJ}, which is (from his perspective) 7 winning combos and 8 losing combos (of which 4 are flush + gutshot draws: A♣ with any of the other 3 Ks and A♥K♣ ).

Unfortunately a half-pot c-bet is bad here, because you burn money against the 7 winning combos, you give favourable odds to the 4 drawing combos, you get nothing from the other 3 AK combos and at best you get paid by A♥Q♥. If you're going to bet you need to bet bigger to force the 12-out draws to fold, but then you're paying too much to the winning combos, unless you think he won't check the flop with QQ or JJ (which he probably shouldn't). There is also the risk that with such a strong draw he may x/r and you're forced to fold.

I think this is a tricky spot. I don't like to give him a free card, but equally betting could well be -EV. At the table I would be betting the pot, but having analysed it I fear this may be an error and the safer course is to check.

As played, this is a good fold.