God he's repping so thin. What is your image? Does he think he can push you off a hand? Would he try? If you think he could turn a 99ish hand into a bluff by repping the A then you have to call turn & let him continue on the river.
If not then I think it is a turn fold.
Let's face it his preflop flatting range is very tight(2%). Maybe a little looser on an overcall. Probably 4-5%. He squeezes AQ here and rarely if ever has Axs. I'd say his range is 99-22, QJs+, KJs, AJs.
After the flop his range is: 44, 66-99, KQs(discounted) & QJs
After the turn his range is: 44, 66, PP bluffs, QdJd, KdQd
Pokerstove says roughly 50/50 with that range and that includes a few bluffs with equity, but no air.
I can see a turn FOLD. I don't think I can do it during the game flop and you image better be squeaky clean. If you get out of line at all this is a call.