I don't think I played this well on the flop, but I'm not sure if I should have given up on the turn. I flop two pair w/ board that could have made a broadway for the BB who 2-barrels. I thought his twice-the-pot flop bet was suspicious. I don't have reads or tons of stats on the villain, but he seems nitty (17/3/0.8).

Thoughts?

Grabbed by Holdem Manager
NL Holdem $0.05(BB) Replayer
SB ($2.36)
BB ($5.07)
UTG ($5.26)
UTG+1 ($4.25)
UTG+2 ($4.98)
MP1 ($12.36)
MP2 ($3.66)
Hero ($5.07)
BTN ($11.09)

Dealt to Hero K T

fold, fold, fold, fold, fold, Hero raises to $0.25, fold, fold, BB calls $0.20

FLOP ($0.52) Q T K

BB bets $1, Hero calls $1

TURN ($2.52) Q T K Q

BB bets $3.82 (AI)

Hero???