Villain is Kilmarta, I have him at 13/9/2 and he seems pretty damn nitty postflop. The 3bet gave odds for sethunting, so he can have any of the sets, particularly JJJ and 999. I don't think he'd do this with QQ, maybe KK although I assume he'd often 4bet KK. There are plenty of draws he can have, albeit a few less because I hold the Ac.

Shove? or Fold?

PokerStars No-Limit Hold'em, $1.00 BB (9 handed) - Poker-Stars Converter Tool from FlopTurnRiver.com

UTG+1 ($160.15)
MP1 ($103.60)
MP2 ($104.85)
MP3 ($121.45)
CO ($119.90)
Button ($99.50)
SB ($100.50)
Hero (BB) ($341.75)
UTG ($94.05)

Preflop: Hero is BB with A, A
6 folds, Button raises to $3, 1 fold, Hero raises to $11, Button calls $8

Flop: ($22.50) 5, J, 9 (2 players)
Hero bets $15, Button raises to $47, Hero ?