I don't see him three-betting you with a smaller pair or A/Q. That means he probably doesn't have a set.
A/A and K/K are what we're fearing at this point.
The big problem is that you checked the flop. That sorta tells
him "My A/K missed" and with aggression factor like that he's going to raise that apparent weakness.
Had you opened, you'd have a lot better info on the strength of your hand. Even doing a check/raise on the flop would have made our decision easier.
I'd normally just fold and scold myself, and lick my wounds, but his stats... 15/14/infinite? When he plays he plays hand. There's a good chance you're best here. But by the time this had is over he'll be stacking and you'll have a hard decision to make.
If I were in your shoes I'd fold unless I specifically saw him be this aggressive on every street in earlier hands.