I'd just take a flop, if you want to 3 bet do it much bigger. He's turbo folding Ax boards if you're ahead.

As played TLR is right, put a real bet out on flop, you'd make this play with AA never % on that board. Then you call and confirm exactly your two cards. Either ship or fold flop as played.

As played I don't see why the 9 is bad, if it was good to chase an A/K on the flop it's still good now, he didn't have a gutter and the pot is massive.

this whole hand looks like you're making plays based on formulas and plans(I three bet AK, I c bet small), play in a way that allows you to profitably bet your hand or bluff - hopefully both.