I'd just get it in pf tbh. As played, he's continuing like his whole 3-betting range on that board (except maybe AA). I'm not folding to a half pot bet yet.

Consider if you flat what happens on the turn? What's he going to fire again with given that you raised in EP, flatted a 3-bet and called a bet on an A-high flop?

AK maybe some AQ and sets will bet again.
Weaker A's may c/c thinking your range has a lot of hands that arent folding that beat him.
What about hands you beat TT-QQ, maybe 88? Are they really firing a blank turn?

I think I'd call flop planning to check behind turn or fold and see what happens on river if you get there.