Villain is an unknown. I put him on Kx/worse Q/flush or str8 draw. Do we make a big raise to charge flush draws and get value from worse Q's or call and get value from K's?

Full Tilt No-Limit Hold'em, $4 BB (9 handed) Hand History Converter Tool from FlopTurnRiver.com (Format: FlopTurnRiver)

Button ($388)
SB ($62)
BB ($453.25)
UTG ($191.60)
Hero ($420.90)
MP1 ($400) sitting out
MP2 ($107.90)
MP3 ($400)
CO ($295.70)

Preflop: Hero is UTG+1 with Q, J.
1 fold, Hero raises to $14, 5 folds, BB calls $10.

Flop: ($30) K, Q, Q (3 players)
BB checks, Hero bets $24, BB raises to $54, Hero...