I don't like that he check/raises the flop. He's dumb or strong.
With the pre-flop action I don't put him on 7/7, 9/9, Q/9, or Q/7. If you are behind, you're behind to Q/Q or A/A.
I think he's trying to overplay his A/Q with the check/raise. If he had A/A I think he'd have re-popped you pre-flop. Q/Q is possible, but with a Q on the board it's not nearly as likely as A/Q.
I say shove.
I had a similar situation last night, where the guy did the same check/raise move with top pair to the board and an Ace kicker. My hand was better, and he called-my shove (6-max $25NL, for a $55+ pot).
I checked and I do have a few hands against poker4fun007. He was pretty tight,14% VP$IP, but that's based so few hands (17) that it's almost meaningless.