Preflop
Villain has 190$ and I have him covered. He is running at 24/11/3.7 over 150 hands. I've been pushing him a little on most tables by 3-betting, few 4-bets and quite a few blind steals. So i can assume is his at least a bit agitated. Table is 4 handed. Villian limps in CO and i raise to 10$. Villain is the only caller.

Flop
Pot: 23$
He checks I decide to CB to standard 17$. He just calls.

Turn
Pot: 57$
He checks and I decide to bet. He is not a frequent floater but he might be drawing here. If he has a weaker Kx besides AK i could get him to fold. So i bet 41$ and he immediately pushes all in for remaining 163$. Now..What could be his hand range here? I have no special reads on how he plays sets(If he is willing to c/c them on drawy board). Is it better to check that turn and be faced with a 30-40$ river bet that i basically cant call?
tnx

Betting the turn is best here.

When you bet the turn and you're behind, he'll usually raise you on that board and you'll know you're no good. If he calls you've most likely charged his draw and you can check behind on the river.

If you're behind and check, you're most likely going to end up paying one bet on the river when it bricks anyways. If you're ahead and you check, you just gave him a free chance to draw.