100NL - Flopped set - is checking turn here horrible????<>

[WC3V]

Villain is decent running at 20.8/14.4/4.33 over 440 hands.
I got the feeling he was floating me light at times. I guess the standard is to fire turn again, is a check here, obv. looking to CR AI horrible here?????

Having said that, is the river double check the right play given we now expect him to bet a missed draw and value bet a weakish king he might have flat called on the flop?

Cheers

Full Tilt Poker, $0.50/$1 NL Hold'em Cash Game, 5 Players
LegoPoker Hand History Converter

BTN: $100
SB: $99
BB: $39.55
Hero (UTG): $166.60
CO: $333.40

Pre-Flop: 8[img]/images/graemlins/heart.gif[/img] 8[img]/images/graemlins/club.gif[/img] dealt to Hero (UTG)
<font color="red">Hero raises to $4</font>, CO calls $4, BTN calls $4, SB folds, BB calls $3

Flop: ($16.50) 6[img]/images/graemlins/club.gif[/img] 8[img]/images/graemlins/diamond.gif[/img] K[img]/images/graemlins/club.gif[/img] (4 Players)
BB checks, <font color="red">Hero bets $11</font>, CO folds, BTN calls $11, BB folds

Turn: ($38.50) 3[img]/images/graemlins/diamond.gif[/img] (2 Players)
Hero checks, BTN checks

River: ($38.50) 3[img]/images/graemlins/spade.gif[/img] (2 Players)
Hero checks, BTN checks