AA 3bet pot on wet board

This is FR, he’s in EP, and his stats look tight. I think we can assume he’s only opening good PPs and some other strong hands. His defending range against your 3-bet is therefore pretty small: maybe 99 - QQ, AQ, possibly AK if he prefers not to 4-bet that (but we block many Ax combos, of course).

He should have very few flushes, so could we get some value from a worse PP with a small turn bet? I’m not sure.

I doubt there’s a value bet on the river. He’s only going to call (or raise) with 55 or T9 and fold anything else. Having said that, I’d be a bit surprised if he defended those hands preflop, but it seems pointless to bet if we’re never getting called by worse.

Pretty much agree with Michael.

On the turn we can bet. He's probably called the flop with the range proposed by Michael, and lots of it contains a random spade. He'll call the turn with a pair+FD, such as QQs JJs ect. If he raises us it's an easy fold and we know where we stand, but if we check back and he bets big on the river it's a tough spot.
I'd bet 1/2 pot on the turn and then give up.

I would bet the pot on intuition, not much chance of a flush, would his range include 5s paired. if he had a set on the flop he would have raised more but im only a beginner

I don't think the flop bet is too small, to me it looks more like too big.
Sure the board is drawy but this is full ring, we play vs tight player opening from UTG+2 and calling a 3bet. I don't think it hits villains range very well.
I think the turn should be bet because of the reasons DecMate mentioned.

The flop bet is big, having in mind that this is a 3b pot.
I agree with the turn bet.
On river when the straight got there too I would xb.