PS $.5/1 Pocket AA -- Is this river raise good?

[Vex]

When playing this hand, I wavered after the flop. I know I should have raised the turn. I put my opponent on a big king, but I got scared of KK or a random trey. Then, on the river, I thought I'm ahead often enough for the raise to be a profitable move. Was it?

PokerStars 0.50/1.00 Hold'em (8 handed) converter

Preflop: Hero is MP1 with A[img]/images/graemlins/heart.gif[/img], A[img]/images/graemlins/club.gif[/img].
UTG calls, <font color="#666666">1 fold</font>, <font color="#CC3333">Hero raises</font>, <font color="#666666">4 folds</font>, <font color="#CC3333">BB 3-bets</font>, <font color="#CC3333">UTG caps</font>, Hero calls, BB calls.

Flop: (12.50 SB) 3[img]/images/graemlins/heart.gif[/img], K[img]/images/graemlins/club.gif[/img], 3[img]/images/graemlins/club.gif[/img] <font color="#0000FF">(3 players)</font>
BB checks, <font color="#CC3333">UTG bets</font>, <font color="#CC3333">Hero raises</font>, BB folds, <font color="#CC3333">UTG 3-bets</font>, <font color="#CC3333">Hero caps</font>, UTG calls.

Turn: (10.25 BB) 7[img]/images/graemlins/spade.gif[/img] <font color="#0000FF">(2 players)</font>
<font color="#CC3333">UTG bets</font>, Hero calls.

River: (12.25 BB) 2[img]/images/graemlins/spade.gif[/img] <font color="#0000FF">(2 players)</font>
<font color="#CC3333">UTG bets</font>, <font color="#CC3333">Hero raises</font>, <font color="#CC3333">UTG 3-bets</font>, Hero calls.

Final Pot: 18.25 BB