100NL flopped flush; how to extract on river?

[TimM846]

I've been lurking and posting for a while now but this is the first hand I'm posting...the first of many [img]/images/graemlins/laugh.gif[/img]

Reads: It's my second orbit at the table and villian is unknown, but two hands ago he raised a limper and then overbet all in on the flop for about 8 times the pot.

Hero is SB with 6 [img]/images/graemlins/spade.gif[/img]5 [img]/images/graemlins/spade.gif[/img]

Pre-flop:

UTG folds. Villian calls. CO folds.
BTN folds. Hero (SB) calls. BB checks.

Flop (board: 9 [img]/images/graemlins/spade.gif[/img] A [img]/images/graemlins/spade.gif[/img] 7 [img]/images/graemlins/spade.gif[/img]):

Hero bets $3. BB folds. Villian calls.

Turn (board: 9 [img]/images/graemlins/spade.gif[/img] A [img]/images/graemlins/spade.gif[/img] 7 [img]/images/graemlins/spade.gif[/img] T [img]/images/graemlins/heart.gif[/img]):

Hero bets $9. Villian calls.

River (board: 9 [img]/images/graemlins/spade.gif[/img] A [img]/images/graemlins/spade.gif[/img] 7 [img]/images/graemlins/spade.gif[/img] T [img]/images/graemlins/heart.gif[/img] Q [img]/images/graemlins/diamond.gif[/img]):

Hero checks. Villian checks.

Analysis: My biggest leak recently has been to check my good hands on later streets with the intention of calling or raising, rather than leading out. The "flop bet, turn c/r against a floater" has been working so well that I've taken a similar approach on hands where such action isn't warranted. Should I bet this river for value, and if so, how much should I bet?