$50+5 Facing Min-Reraise with AK

[Poisson7]

Stars $50+5, level 3 blinds are t25-50. Here is on the Button with AKo with average stack of t1600. All the other players relevant in this hand have about same. Please critique all parts of play! I feel like I botched this hand.

Villain in MP limps and CO raises to t150.
Hero reraised 250 to t400.
Villain min-re-raises to t650. CO folds.
Hero...? I called

Flop comes Q-X-X.
Villain thinks for a while then pushes.
Hero...? (I think this is an easy fold, so it's really my preflop play that I'm curious about, but would love critiques of my flop play).

I figure to min-reraise into two players Villain has to have AA-QQ. But why would any of those hands push on the flop? Advice, plz!

[TruFloridaGator]

Tough call, I would fold too though, could be overplayed JJ afraid of the Q.

[Phil Van Sexton]

I like the raise to 400 PF.

Of course, you must call the min raise, but I'd be suprised if he didn't have AA. He probably pushed on the flop because there was so much money in the pot that he just wanted to take it down so that PokerStars cant screw him on the river.