8/16 live: button play flush river decision

[pureCra2z]

juicy 8/16 game.. usually 6~7 limpers in a raised pot pf. Villain in this hand has been playing >40% of hands for the previous 3 orbits but have been catching cards and only been showing down big pf hands that that hit the board. I've raised Villain twice in the last few orbits ip and reraised his flop bets with tp when theres <4 in the pot on the flop, he 3 betted each both times and I folded on turn and h showed down flopped set and KK.

Hero(Button): $900ish
SB: 200ish
Villain (BB): 1k ish

folded around pf(only time this happened for the whole 5 hours i was there)

Pre-Flop: Q[img]/images/graemlins/diamond.gif[/img] 6[img]/images/graemlins/diamond.gif[/img] dealt to Hero (Button)
Hero bets, SB calls, BB reraises, Hero calls, SB calls. ($48pot)

Flop: K[img]/images/graemlins/diamond.gif[/img] 8[img]/images/graemlins/diamond.gif[/img] 4[img]/images/graemlins/diamond.gif[/img]
SB checks, BB checks, Hero bets, SB calls, BB reraises, Hero 3 bets, SB calls, BB caps, Hero,sb call ($144pot)

Turn: 3[img]/images/graemlins/club.gif[/img]
SB checks, BB bets, Hero reraises, SB folds, BB callsv($208 pot)

River: K[img]/images/graemlins/club.gif[/img]
BB checks, Hero ????

b/f? b/c? check?