[Mathieu]

I'd 3 bet pre-flop and lead the flop.

Given that you just called, I like the checkraise and I would bet the turn and river for value.

Villain did not raise you after the flop so it is likely you have the best hand. It's possible that villain has a small pocket pair and he is worried that he is beat.
But the overcards are wore likely.

After villain called the turn, it is more likely that he has a pocket pair but far from guaranteed since many unknowns would call down with A high on this board.

So you have to bet the river since you are out of position, and if you check he will likely check a weaker Ace, and bet a pocket pair. If you bet he will often call you with a weaker Ace.