($50 NL) How cheaply can you get away from this QQ in the bb?

Bodog $50 nl

This hand made me cringe. At what point would you dump this QQ? How do you play this?

Relevant stacks
utg $65
villain (on button)$140
hero (bb) $60

I just moved to the table about 30 minutes before, have not seen villain show down any hands or how he built up his stack.

Hero dealt QdQs in bb

PREFLOP
utg raises to $2, villain reraises to $5.25 on button, Hero calls and already hates it, utg folds.

FLOP (pot $11) 7d 3h 7s
Hero checks, villain bets $11, Hero...?

Preflop I think I have to call, it's much to weak to fold here and we are all deep enough to be calling for implied odds on hitting my set even if I know villain has AA or KK. Is my thinking right here?

On the flop, I think maybe I should have led out for half to 3/4 pot, but I didn't want to get just called and try to figure out where I'm at, so I want to see villains action first. When he pots it, I am fairly certain I am beat. Should I fold at this point? I feel my check was terrible because now I can't put in any raise without severely crippling my stack, I'm not comfortable pushing because I feel I am behind, and if he does come over the top of a raise I will be certain I am beat.

Any words of wisdom will be greatly appreciated, I just hated the spot I was in here.