KK facing 3 suited board on turn

Villain was new to the table so I had no reads whatsoever. When he called my flop raised I feared he might have made a set or just a loose caller drawing to the flush. My question is, was betting the turn the right move? Or should I have just checked behind? And what should I do if he had just called and the river was a blank for me?


Party Poker No-Limit Hold'em, $ BB :#A500AF(Villain)/ (8 handed) FTR converter on zerodivide.cx

BB :#A500AF(Villain)/ ($24.50)
UTG ($24.20)
UTG+1 ($4.25)
MP1 ($22.20)
MP2 ($25.30)
CO ($18.85)
Hero ($27.40)
SB ($25.15)

Preflop: Hero is Button with K[img]/images/graemlins/club.gif[/img], K[img]/images/graemlins/spade.gif[/img]. SB posts a blind of $0.10.
<font color="#666666">3 folds</font>, MP2 calls $0.25, <font color="#666666">1 fold</font>, <font color="#CC3333">Hero raises to $1</font>, <font color="#666666">1 fold</font>, BB :#A500AF(Villain)/ calls $0.75, MP2 calls $0.75.

Flop: ($3.10) 2[img]/images/graemlins/spade.gif[/img], 5[img]/images/graemlins/spade.gif[/img], 9[img]/images/graemlins/club.gif[/img] <font color="#0000FF">(3 players)</font>
<font color="#CC3333">Villain bets $3</font>, MP2 folds, <font color="#CC3333">Hero raises to $8</font>, Villain calls $5.

Turn: ($19.10) 6[img]/images/graemlins/spade.gif[/img] <font color="#0000FF">(2 players)</font>
Villain checks, <font color="#CC3333">Hero bets $10</font>, Villain folds.

Final Pot: $29.10