Tough situation w/QQ semi-deep

[schlucky1]

.25/.5 NL ($50 max) 6-man.
Villain is 34/16/10 over about 250 hands. Obviously very aggressive. He 3-barreled against me earlier w/AK afer reraising me pf from SB, and I made a tough river call w/JJ after sensing weakness on his flop and turn bets. After this, I don't really see him firing this light again, although he is super aggro. Anyway, this hand comes up:

We both have about $80

Hero dealt Q [img]/images/graemlins/spade.gif[/img]Q [img]/images/graemlins/diamond.gif[/img] on Button

Hero raises to $2.5 after one limper, Villain re-raises to $6.5 from BB, hero calls $4

Flop ($13.75): 4 [img]/images/graemlins/spade.gif[/img]6 [img]/images/graemlins/diamond.gif[/img]6 [img]/images/graemlins/spade.gif[/img]

Villian bets $11, Hero raises to $22, Villain insta-shoves, Hero folds

Given his aggression, I guess it's possible for him to have 99-JJ, but he shoved so fast I had to think AA or KK, possibly A [img]/images/graemlins/spade.gif[/img]K [img]/images/graemlins/spade.gif[/img]

I guess my question is how do I make this hand play easier? I think if I reraise pf to about $18-22, I take control and have a better chance to define his hand. This allows me to fold if he shoves, but if he just calls and then check-shoves to my flop bet I'm in another tough spot. I don't really like my min-raise on the flop, but if I make a standard raise I have to go to the felt. I guess I could have just folded, but I don't really like that here either. Any thoughts?