Villian is 38/12, so I figured there was at least some chance he didn't have AA. I didn't want to 3-bet PF, since then the only hand that is calling or reraising is AA (I think). So I tried to adopt a line that would get the most value out of the times villian has less than AA. In retrospect, it looks pretty ugly. What should I have done?

PokerStars No-Limit Hold'em, $0.25 BB (9 handed) Hand History Converter Tool from FlopTurnRiver.com (Format: FlopTurnRiver)

MP1 ($34.90)
MP2 ($23.80)
MP3 ($39.15)
Hero ($44.85)
Button ($41.70)
SB ($33.80)
BB ($28.40)
UTG ($6.65)
UTG+1 ($8.35)

Preflop: Hero is CO with K, K.
1 fold, UTG+1 calls $0.25, MP1 calls $0.25, 2 folds, Hero raises to $1.25, 2 folds, BB raises to $3.75, UTG+1 folds, MP1 folds, Hero calls $2.50.

Flop: ($8.10) Q, 4, 5 (2 players)
BB bets $4, Hero raises to $41.1