Not sure if I played this one correctly

PokerStars 0.10/0.20 Hold'em (8 handed) converter

Preflop: Hero is UTG+1 with 9[img]/images/graemlins/club.gif[/img], 9[img]/images/graemlins/diamond.gif[/img].
UTG calls, <font color="#CC3333">Hero raises</font>, <font color="#666666">2 folds</font>, CO calls, Button calls, <font color="#666666">1 fold</font>, BB calls, UTG calls.

Flop: (10.50 SB) A[img]/images/graemlins/heart.gif[/img], 2[img]/images/graemlins/heart.gif[/img], 2[img]/images/graemlins/club.gif[/img] <font color="#0000FF">(5 players)</font>
BB checks, UTG checks, <font color="#CC3333">Hero bets</font>, CO folds, <font color="#CC3333">Button raises</font>, BB folds, UTG folds, <font color="#CC3333">Hero 3-bets</font>, <font color="#CC3333">Button caps</font>, Hero calls.
Button was the type of player who would have 3-bet a big A, and I was pretty sure he would have folded a weak A, so I couldn't put him on an A at all. I'd been on a "mini-rush", raising PF and winning a lot of hands. I thought that maybe he was trying to catch me in a bluff. The pot was giving me 15.5-1 to catch my 4 outs if I was behind.(If I did my math right...)

Turn: (9.25 BB) 9[img]/images/graemlins/heart.gif[/img] <font color="#0000FF">(2 players)</font>
<font color="#CC3333">Hero bets</font>, Button calls.
Should I have gone for a c/r here? At the time, I was thinking 2 things: that I didn't want to miss a bet, and that I wanted to keep him in the hand and raise on the river.

River: (11.25 BB) 8[img]/images/graemlins/heart.gif[/img] <font color="#0000FF">(2 players)</font>
<font color="#CC3333">Hero bets</font>, <font color="#CC3333">Button raises</font>, <font color="#CC3333">Hero 3-bets</font>, <font color="#CC3333">Button caps</font>, Hero calls.

Final Pot: 19.25 BB
Did I play this correctly?