Good laydown with AA?

[Mr. Curious]

Live $12/24 game
9 Handed

BB has been riding one hell of a lucky streak. He's loose and aggressive and will chase postflop.
MP3 has a horseshoe up his butt. Miracle cards have been dropping like flies for him and he has been running over the table. He's loose and aggressive, but decent post flop.

Hero is in the CO with A[img]/images/graemlins/club.gif[/img]A[img]/images/graemlins/spade.gif[/img]

Preflop: UTG folds, UTG+1 folds, MP1 calls, MP2 folds, MP3 calls, Hero raises, Button calls, SB folds, BB calls, MP3 calls, CO calls

Flop: 5[img]/images/graemlins/spade.gif[/img]7[img]/images/graemlins/spade.gif[/img]7[img]/images/graemlins/heart.gif[/img] (5 players)
Pot: (10 SB)

On the flop, BB looks like he is hyperventilating and last time he acted this way, he showed down a strong hand. He looks at me like he is begging me to bet so he can check raise.

It is checked around to me and I bet (I know there are draws out there, but would it be safer to check based on BB's behavior and protect my hand on the turn instead?).

Button folds, BB raises, MP1 folds, MP3 calls two cold, I call.

Turn: Q[img]/images/graemlins/club.gif[/img] [5[img]/images/graemlins/spade.gif[/img]7[img]/images/graemlins/spade.gif[/img]7[img]/images/graemlins/heart.gif[/img]] (3 players)
Pot: (8 BB)

BB bets, MP3 raises, Hero folds...