I think its hard to tell whether he had the flush or bluff, he knows hes bluffing if he has a weaker A, he knows (thinks) you havent hit the flush bc he cant see you been so aggressive when it shows, big chance for him to bluff. I think you created too much of a pot on the turn when the scary diamond showed, giving him a chance to make a realistic bluff, i cannot see him having any ace at all unless he has AA or he is poor and thinks he is in front with AJ but given that his vp/pr ratio is high hes obviously not a fish, the reason i cant put him on an ace is bc i cant see him check calling the flop and checking back to you on the turn with an ace bc it gives him no info. I think the way you played it i would have to fold, i would say next time you're in this position defo check to get your free card and weigh it up again. I mean...what can you be beating..... not lots, a bluff or weak ace ( as above) no way has he got another PP (unless AA or 99) bc he wouldn't raise you after a 3 bet pf. (gotta eliminate 33 given his vp lowish and the call on the flop)
My guess(es) is he overated his A9 and flopped the dream... he had 99 although id rather say he had AA, im not sure now i can put him on a flush either, the board is paired.. would he give you the chance to check and land a FH? Don't think so, i'm eliminating the hnds as i type lol.. scratch AA, im daft, defo reraise pre flop unless hes crazy.
Im thinking he either was weak pf and had A9, checked hoping you'd bet your AK (what he mighta thought) and waited for the turn bet, off you, to raise it.
OR
He has 99 and is basically trying to get as much of you as he can.
OR (im gonna have to say this is my fave)
He has picked up on the diamond on the turn and used it, along with the two 9s showing, and pulled a nice bluff.
The mistake was betting the turn i think, check the turn, although you will probably have the same dilemma on the river, so.... maybe (unless he bluffed) you did the 'cheapest' thing (if you folded on the turn after his raise) by getting check raised bc if you checked the turn i think it would have been very hard to fold the river, even with a big bet.
AQ is a hard hand to play.. pot control is probably your best tactic here.