NL25SH TPTK on the Turn vs paired board

[stever1k]

PokerStars No-Limit Hold'em, $0.25 BB (6 handed) Poker Stars Converter Tool from FlopTurnRiver.com (Format: 2+2 Forums)

BB ($20.25)
Hero ($28.55)
MP ($16.25)
CO ($25.35)
Button ($21.40)
SB ($64.55)

Preflop: Hero is UTG with Q[img]/images/graemlins/club.gif[/img], K[img]/images/graemlins/heart.gif[/img].
<font color="#CC3333">Hero raises to $1</font>, <font color="#666666">3 folds</font>, SB calls $0.90, <font color="#666666">1 fold</font>.

Flop: ($2.25) 2[img]/images/graemlins/heart.gif[/img], 7[img]/images/graemlins/diamond.gif[/img], 7[img]/images/graemlins/spade.gif[/img] <font color="#0000FF">(2 players)</font>
SB checks, <font color="#CC3333">Hero bets $1.5</font>, SB calls $1.50.

Turn: ($5.25) Q[img]/images/graemlins/heart.gif[/img] <font color="#0000FF">(2 players)</font>
SB checks, Hero checks.

River: ($5.25) 2[img]/images/graemlins/diamond.gif[/img] <font color="#0000FF">(2 players)</font>
SB checks, <font color="#CC3333">Hero bets $3</font>, SB calls $3.

Final Pot: $11.25

I check this Turn for pot-control and bluff induce, the board allows no draws, except the backdoor flush which I'm not afraid of.

Villain is 31/16/1 (VPIP/PFR/AF) for ~50 hands.