$100nl QQ in 3-bet hand

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

MP1 ($177.65)
MP2 ($197.35)
MP3 ($179.20)
CO ($112.45)
Hero ($98)
SB ($17.55)
BB ($115.55)
UTG ($64.10)
UTG+1 ($76.60)

Preflop: Hero is Button with Qhttp://www.flopturnriver.com/phpBB2/...es/diamond.gif, Qhttp://www.flopturnriver.com/phpBB2/...iles/spade.gif.
1 fold, UTG+1 raises to $4, 2 folds, MP3 calls $4, 1 fold, Hero raises to $16, 2 folds, UTG+1 calls $12, MP3 folds.

Flop: ($37.50) 6http://www.flopturnriver.com/phpBB2/...iles/heart.gif, 7http://www.flopturnriver.com/phpBB2/...iles/heart.gif, 6http://www.flopturnriver.com/phpBB2/...miles/club.gif (2 players)
UTG+1 checks, Hero ...

First orbit and no stats/reads on villain. Villain has $60 behind.

Was the 3-bet preflop bad? I'm stuck in a spot where I feel like I'm behind a lot and can't get away or something.

As played, do I bet smallish ~half pot to make AK think it has fold equity to try to get some more value or what?