Villain is 22/2 over 250+ hands.

PokerStars No-Limit Hold'em, $0.05 BB (7 handed) - Poker-Stars Converter Tool from FlopTurnRiver.com

CO ($1.60)
Button ($10.73)
SB ($4.03)
BB ($5.99)
Hero (UTG) ($5.24)
MP1 ($9.84)
MP2 ($9.50)

Preflop: Hero is UTG with Q, Q
Hero bets $0.20, 5 folds, BB calls $0.15

Flop: ($0.42) 5, K, 2 (2 players)
BB checks, Hero bets $0.25, BB calls $0.25

Turn: ($0.92) 3 (2 players)
BB checks, Hero ?

I find myself having trouble with these spots quite often. I don't want to give him a free card because of all the draws, but I don't want to bet into a K either.