poker.com $25nl, .10/25 blinds

Hero has about $20
Villain2 covers

Hero has A[img]/images/graemlins/spade.gif[/img]K[img]/images/graemlins/heart.gif[/img] on the button
limps around
Hero raises to $1.20
2 callers

Flop: ($4) T[img]/images/graemlins/heart.gif[/img]7[img]/images/graemlins/club.gif[/img]T[img]/images/graemlins/club.gif[/img]
villain 1 checks
villain 2 checks
Hero bets $3
villain 1 folds
villain 2 calls

Turn: ($10) 3[img]/images/graemlins/diamond.gif[/img]
Villain 2 checks
Hero bets $6
Villain 2 calls

River: ($22) Q[img]/images/graemlins/heart.gif[/img]
Villain 2 checks
Hero checks

Thoughts?

I put the villain on a draw, and was hoping to bet him out on the turn.

Is the river check awful? Should I have checked the turn instead of betting? Bet more on the turn?