50 NL - QQ on AAK flop

[Arcturus]

This is my ninth hand at the table. This is villian's (UTG) first hand at the table.

PokerStars No-Limit Hold'em, $0.50 BB (6 handed) Hand History Converter Tool from FlopTurnRiver.com (Format: 2+2 Forums)

SB ($77.60)
BB ($23.20)
UTG ($46)
MP ($31.20)
CO ($6.95)
Hero ($39.25)

Preflop: Hero is Button with Q[img]/images/graemlins/spade.gif[/img], Q[img]/images/graemlins/heart.gif[/img]. UTG posts a blind of $0.75.
UTG (poster) checks, MP calls $0.50, <font color="#666666">1 fold</font>, <font color="#CC3333">Hero raises to $3.5</font>, <font color="#666666">2 folds</font>, UTG calls $3, MP folds.

Flop: ($8.50) K[img]/images/graemlins/club.gif[/img], A[img]/images/graemlins/spade.gif[/img], A[img]/images/graemlins/diamond.gif[/img] <font color="#0000FF">(2 players)</font>
UTG checks, <font color="#CC3333">Hero bets $6</font>, UTG calls $6.

I c-bet almost always, but the call on this board is freaking me out.

Turn: ($20.50) J[img]/images/graemlins/diamond.gif[/img] <font color="#0000FF">(2 players)</font>
UTG checks, Hero checks.

Should I fire a second barrel or just give up?

River: ($20.50) J[img]/images/graemlins/club.gif[/img] <font color="#0000FF">(2 players)</font>
<font color="#CC3333">UTG bets $36.25 (All-In)</font>, Hero folds.