AA on paired board

[jumbojacks]

PokerStars No-Limit Hold'em, $0.50 BB (5 handed) internettexasholdem.com

Button ($79.70)
SB ($87.80)
BB ($49.90)
UTG ($49.25)
Hero ($50.55)

Preflop: Hero is MP with A[img]/images/graemlins/heart.gif[/img], A[img]/images/graemlins/club.gif[/img].
<font color="#666666">1 fold</font>, <font color="#CC3333">Hero raises to $2</font>, <font color="#666666">2 folds</font>, BB calls $1.50.

Flop: ($4.25) 2[img]/images/graemlins/diamond.gif[/img], T[img]/images/graemlins/diamond.gif[/img], T[img]/images/graemlins/spade.gif[/img] <font color="#0000FF">(2 players)</font>
BB checks, <font color="#CC3333">Hero bets $3</font>, <font color="#CC3333">BB raises to $8</font>, Hero calls $5.

Turn: ($20.25) 5[img]/images/graemlins/diamond.gif[/img] <font color="#0000FF">(2 players)</font>
BB checks, Hero...

BB is pretty LAG and tricky 30/20 but his plays are too polarized with either being nuts/bluff. I been playing pretty TAG but I've been starting to open a bit more and play much more loosely. His check-raise here is either a T/22 or air/flush draw like 50/50. Do I bet this turn? If so, how much? I'll probably fold if I get check-raised again since its really unlikely he has the balls to pull that off w/ air and he's not a good enough player to read me for an overpair here.