The way I played this hand is pretty read dependend, but here it is anyway.
Villain was 55/15/2 over 80 hands.
My notes are: Fish, value bet, autopots paired flops
I have seen him raise and call with marginal hands. I have folded twice when he pottet a paired flop after he called my button raise from the blinds. I checked the flop as I see myself miles ahead of the fish's range and want to show weakness against him. Plus I don't like to get reraised by BTN who is unknown to me. As he checked behind on the flop and I turned oesd I am just trying to milk the fish (does this phrase make sense?).
Everest 0.5/1$ 6 handed
BTN: $101.50
SB: $370.50
BB: $74.61
UTG: $100.00
MP: $66.30
Hero (CO): $99.50
Pre Flop: Hero is CO with K

Q

2 folds, Hero raises to $3.5, BTN calls, 1 fold, BB calls $2.5
Flop: ($10.50) K

T

3

(3 players)
BB checks, Hero checks, BTN checks
Turn ($10.50) J

(3 players)
BB bets 11$, Hero raises to 22$, BTN folds, BB raises to 71.11$ all in, Hero calls