KK after a flop cap (again)

[mlb3zr]

PokerRoom hands don't seem to work well with the converter, but here's how the hand went. Villain is really loose/passive. After the flop cap, I'm convinced he's got the 6 (he's not so passive that he wouldn't have raised preflop with big pairs). On the turn, my backdoor flush draw goes away, so now I'm confused: do I check/call down, hoping for my miracle 2 outer or that he's making some really out of character bluff? Do I lead the turn and fold to a raise, now as sure as I can be that he's got the 6? Do I check/fold the turn? What do you think?
Thanks! mlb

PRE-FLOP (9 SB)
2 folds, UTG+2 calls $0.50, MP1 (post) checks, 3 folds, button calls $0.50, hero (SB) (K[img]/images/graemlins/spade.gif[/img], K[img]/images/graemlins/diamond.gif[/img]) bets $0.75, BB folds, limpers and post call.

FLOP (18 SB)[board cards 6[img]/images/graemlins/heart.gif[/img],6[img]/images/graemlins/spade.gif[/img],10[img]/images/graemlins/spade.gif[/img] ]
Hero bets $0.50, UTG+2 calls $0.50, MP1 folds, button bets $1, hero bets $1, UTG+2 folds, button bets $1, hero calls $0.50.

TURN [board cards 6[img]/images/graemlins/heart.gif[/img],6[img]/images/graemlins/spade.gif[/img],10[img]/images/graemlins/spade.gif[/img],3[img]/images/graemlins/club.gif[/img] ]
Hero...