$55 ITM: Flopped TPWK, scare card hit on Turn and facing 3/4pot bet

[AA suited]

PartyPoker, Big Blind is t300 (3 handed) Converter on pregopoker.com

Button (t2850)
SB (t1450)
HERO (t5700)

Preflop: HERO is in BB with J[img]/images/graemlins/heart.gif[/img] 6[img]/images/graemlins/diamond.gif[/img]
<font color="red">Button raises t600</font>, <font color="gray">SB folds</font>, HERO calls t300

Flop: (t1350) 5[img]/images/graemlins/club.gif[/img] J[img]/images/graemlins/club.gif[/img] 7[img]/images/graemlins/diamond.gif[/img] (2 players)
HERO checks, Button checks

Turn: (t1350) 5[img]/images/graemlins/club.gif[/img] J[img]/images/graemlins/club.gif[/img] 7[img]/images/graemlins/diamond.gif[/img] A[img]/images/graemlins/heart.gif[/img] (2 players)
HERO checks, <font color="red">Button bets t800</font>, HERO? [img]/images/graemlins/confused.gif[/img]

No reads. he was bigstack till i got lucky and doubled through him last hand (my AT vs his AQ).

I was hoping for a check raise on flop, but he checked it through [img]/images/graemlins/frown.gif[/img]

What would you do on the Turn, and why?