Hi Papier.
First of all it seams to me based on the villains limp call OOP and the stack size that he is a fish more on the passive side of the spectrum. I assume he is something like VPIP 50 PRF 10.
That said you need to realize that their raises, check raises especially on the turn carry more weight than if some competent LAG or REG does the same thing.
Against these types of players i am in a bet-fold mentallity with my overpairs. Why you ask ? Its simple. A passive player is not raising TP on this turn. It has to be 2 pair or better. For me its a fold on the turn.
Secondly if you think you are good sometimes on his turn check raise you have to stick to your decision and pay off some rivers if he bets. Lets say you call and the turn and a brick duce rolls of on the riv. You will have to call there. Why you ask again ?
Well lets say you put him on some draws, TP, pair + FD etc.
If your KK is good there then its good on a brick duce.
I see many players call that turn and then fold to a river bet becouse "the bet was too big".
If you call the turn and then fold to every river bet you might as well fold the turn. Its just a matter of thinking that step ahead. What rivers are good for you ? What rivers can you call if you are good on the turn ?
A Queen on the riv is probably the worst hand that could fall down cause now if he did somehow raised with TP( which he didnt 99% of the time + he would probably check raise TP on the flop if he were to raise which he wouldnt 99% of the time
) now he has 3 of a kind.
I guess the major point that i am trying to say is that passive fish arent that likely to make big aggresive moves into a guy who raised 4xBB pre, cbets flop, cbets turn and clearly represents a major hand. They are not going to make to many betting mistakes but will make many calling mistakes.