This hand is a really tough spot really, he could have alot of things depending on what kind of player he is.

He limped and then called your raise pre-flop.

What do people limp in with and call a good sized raise with? Weak suited aces, suited connectors, small pocket pairs. It's unlikely he has AQ as that is certainly not a limping hand IMO. It's possible he has a weaker unsuited A aswell A10, A9 or something.

That flop would really scare me 3 to the flush, he checked and you bet about 2/3 of the pot, he then re-raised you. If he had the nut flush it's unlikely he would re-raise you, though not impossible.

At this point I would put him on a few hands, AsX trying to get 2 free cards (very common move), trying to protect a set of 2s or 4s. Again this is likely with 3 spades on the board, you have to protect your hand. Or he is bluffing, though he min raised so bluffing seems unlikely.

The 2 coming on the turn could mean alot of things, he checked. Did he hit his boat? Did he miss his flush? At this point making a 1/2 pot sized bet might be committing too many of your chips. It's a difficult spot, your best case scenario is that he has 12 outs (3 aces, 9 spades) your worst case scenario is that you have 2 outs. I would probably bet out 1/3 the pot, hope he folds, if he calls and the river is a blank I would check it down if possible or probably fold if he pushes.