Weak play, right?

Full Tilt Poker
No Limit Holdem Ring game
Blinds: $0.10/$0.25
4 players
Converter

Stack sizes:
Hero: $38.85
Button: $48.25
SB: $26.30
BB: $24.75

Pre-flop: (4 players) Hero is UTG with A K
Hero raises to $0.85, Button calls, 2 folds.

Flop: J K 7 ($2.05, 2 players)
Hero bets $1.5, Button calls.

Turn: Q ($5.05, 2 players)
Hero checks, Button bets $3.25, Hero folds.
Uncalled bets: $3.25 returned to Button.

Results:
Final pot: $5.05

No reads.

I'm pretty certain I should bet the turn but, having checked, do I call his bet?

Betting would be easier. He might figure you weak due to your turn check. Hard to say what to do after he bets, you pretty much yielded control. Maybe raise even? I can't say. He might have two-paired his JQ or KQ, or got an AT / 9T straight, or who-the-hell knows. I won't find fault with a fold at this point.

You're bigslikk, you gotta know!