Another AA vs. KK

[Rockymv]

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

[Fnord]

Against a player that loose and aggro pre-flop, I 3-bet this every time pre-flop and am happy to play for 100bb deep stacks.

If he's got AA, good for him. His chip spewing on every other hand he plays earns him my action here.