UB 50NL 3 handed

[Triumph36]

I've been getting decent cards when the table was full, but in the last 10 minutes everyone has left, except 3 people. I've folded to every PFR and have been playing tight. I have about $55 and opponents each have $100.

I get AQ offsuit on the button and raise to $3, hoping that one of my opponents will sense weakness and call with marginal holdings or (maybe) come over the top. SB comes over the top, making it $6.50 to me. I think for a while and call. Flop comes A9Q. SB bets the pot (20 or so), I come back over the top, he lays it down.

I haven't played much ring-game 3 handed, so I was wondering whether or not my line was good. I have two main questions:

Should I have folded, called, or re-raised pre-flop? AQ is a monster at three-handed, so folding with position seemed like a mistake. If I re-raise, he probably folds anything I dominate and calls only with hands that either beat me or I'm in a race with. If I call, I'm paying 1/8th of my stack to try to spike an ace or queen; if he has AK and an ace flops, that's just a tough break for me; I'm not laying down top pair, good kicker three-handed on the flop.

The other question is: Should I have called on the A9Q flop and let him stack himself on the turn? I put him on AK after the big bet so I figured he would've called a raise; he hadn't pot committed himself, but I believe my final bet was only about two thirds of the pot (26 or so on top of 40 total). I definitely thought he'd pay it off with AK, and his bet certainly represented that. I still haven't been able to figure out what he possibly could've been holding that leads out at that flop and folds to a raise. Possibly JJ, KK, or TT hoping that I was calling with a smaller pocket pair or that I'd fold a Q in that spot, but I'm still baffled about his play.