AA Runs Into Four Flush

[ninjaunderwear]

No read here, but I don't think a read would help any in this situation.

Party Poker 1/2 Hold'em (10 handed) FTR converter on zerodivide.cx

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

Flop: (5 SB) A[img]/images/graemlins/diamond.gif[/img], 6[img]/images/graemlins/diamond.gif[/img], 8[img]/images/graemlins/diamond.gif[/img] <font color="#0000FF">(2 players)</font>
SB checks, <font color="#CC3333">Hero bets</font>, SB calls.

Turn: (3.50 BB) K[img]/images/graemlins/diamond.gif[/img] <font color="#0000FF">(2 players)</font>
<font color="#CC3333">SB bets</font>, Hero calls.

River: (5.50 BB) 9[img]/images/graemlins/heart.gif[/img] <font color="#0000FF">(2 players)</font>
SB checks, <font color="#CC3333">Hero ???</font>.

When SB wakes up on the turn four-flush, I quickly called behind. Folding is out of the question. [In hindsight, a raise has some merit.]

If SB caught a flush, he doesn't seem too confident about it on the river. If I bet, any hands that can call me have me beat. However, there is a chance I can fold a 2[img]/images/graemlins/diamond.gif[/img].

In such a small pot, is there any value in betting here? Or should I just take the free showdown? Is it even close?