KK, big pot, turn Ace

Villain is a 54/10 over 43 hands. Never see him 3bet or 4bet. I've seen him try and get trappy with a set ealrier, but nothing else of note. Ftcb 38%, Rcb 25%.

3b calling range is 77+, ATs+, AJ+.

When he calls my flop cbet I figure he has 88, JJ+, AhTh, AhQh, AJ.

When the Ace hits on the turn I want to cry.

I figure any bet from me folds out QQ, and once that's removed from his range I'm like a 6% dog so betting isn't an option. But as half my stack is in I'm looking for justification to not fold. Maybe my range is all wrong. Any thoughts?

Full Tilt No-Limit Hold'em, $0.50 BB (9 handed) - Full Tilt Converter Tool from FlopTurnRiver.com

UTG ($51.95)
UTG+1 ($61.25)
MP1 ($71.75)
MP2 ($47)
MP3 ($70.40)
CO ($60.70)
Button ($56)
Hero (SB) ($58.30)
BB ($53)

Preflop: Hero is SB with ,
4 folds, MP3 bets $2, CO calls $2, 1 fold, Hero raises to $9, 1 fold, MP3 calls $7, 1 fold

Flop: ($20.50) , , (2 players)
Hero bets $16, MP3 calls $16

Turn: ($52.50) (2 players)
Hero??????