Villain is 16-12-4 and has shown nothing to suggest that he's completely stupid. Pre-flop range is pairs, with a tendency towards 99-KK, but 22-88 are possible as well. I don't think he's stupid enough to go broke with 99-KK here.
100bb deep this is easy, "AA is the nuts in a 3-bet pot".
200bb deep and it becomes interesting.
I think the best play is to raise to $28, fold to a push.
BUT, if villain flat calls the raise, then bets the turn for $30-$40 I guess it's an obvious fold?
I called, thinking to re-evaluate on turn.

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

UTG+1 ($100)
MP1 ($50)
MP2 ($100)
Hero ($136.80)
CO ($98)
Button ($186.15)
SB ($99.50)
BB ($211.45)
UTG ($113.75)

Preflop: Hero is MP3 with A, A.
1 fold, MP2 raises to $1.75, Hero raises to $5.5, 4 folds, MP2 calls $3.75.

Flop: ($11.75) 7, 8, 6 (4 players)
MP2 bets $10, hero is all wtf, what are you doing donking into me. You got a set or an overpair? you folded 9T pre, so I'm not scared of the straight. you know i can't fold aces to this bet, what should i do?!?!? aargghh, too much action on the other 12 tables... maybe i fold, nah, that's stupid. so I call to re-evaluate on turn...