Facing Flop Raise 3bet AA

Preflop 3 bet should be smaller (against fish - which might be the case - it can be more than 3,5x). Raising the turn would be overplaying. I think we can call. OTR I prefer folding.

Ooo I love these spots when I happen to call a 3bet with 88 and hit a full house.. I have stacked so many villains OTF when they overplay their overpair
In a single raised pot this flop xr can definitely be a bluff. In a 3bet pot not so likely imo, but it is still possible. Maybe he can have weaker overpairs too. I would call the flop here and probably turn too. But when we get OTR and he puts us all-in, I'm not so sure anymore.
He can have some flushes which were total bluffs OTF but improved. If he has QQ-99 he is overplaying his hand. You have to win this only 25% so I think it might be close.

And about that 3bet size. It is quite big-ish when you consider villain opened only 2.5bb and you are in position.

For 100BB i am not folding ever in this spot. Just calling turn and river is the better play as you keep all his trash and bluffs in. Even if he has a flush draw he would have called your turn shove and the result would have been the same. I like the hand

Finding the best course of action here involves your range and how he perceives it, and how he perceives you. You may be capped, and he might be able to find this out. (Having a few 88/77/87s in your range here would be vital against a good player.) He might mistakenly also do this with an overpair himself. Getting away here is difficult. Turn is the decision point. We don't fold OTR due to small remaining stack.

Edit: If the flop were 7♦:2♠:7♥:, then it is a pretty nice spot to check behind on flop. Multipurpose, with very few drawbacks.