K9s backdoors nut flush, can I get more value on the river?

[Parasurama]

Full Tilt No-Limit Hold'em, $0.50 BB (6 handed) - Full-Tilt Converter Tool from FlopTurnRiver.com

BB ($63.45)
UTG ($73.40)
MP ($67.40)
CO ($50)
Hero (Button) ($75.55)
SB ($48.30)

Preflop: Hero is Button with K, 9
3 folds, Hero raises to $1.75, SB calls $1.50, 1 fold

Flop: ($4) 8, 6, A (2 players)
SB checks, Hero bets $3, SB calls $3

Turn: ($10) J (2 players)
SB checks, Hero bets $6, SB raises to $12, Hero calls $6

River: ($34) 7 (2 players)
SB checks, Hero bets $22, SB calls $22

Total pot: $78 | Rake: $3

I pretty much just started playing a lot of 6max so I didn't have stats on villain. I've gotten the better of him in a few marginal spots so he knows I'm capable of having nothing or a medium strength hand here. Overall he seems to be pretty solid though. C-bet this flop always right? What about turn? Should I just take the free card? I kind of felt like had exactly AJ but I bet anyway because I wanted to build a bigger pot if I hit and because he could still fold some hands that were beating me.

[Ash256]

If he's tight and unlikely to have 78/98-J8 here I check behind on the turn.

It's kinda funny that before you wouldn't try to bluff someone off top pair at 50NL because they were all calling stations, but now you oughtn't try it because no-one believes anyone

[yourfather]

I do a instashove to look bluffy. Villain has like $31 on river so its not even a full pot sized bet.

[griffey24]

I'd shove river, he has a potsize bet left. After he c/r you on the turn his range is very polarized to nonsense that won't call the size of bet you made, or strong hands that will call a potsize bet anyhow.

I'm always double barreling this turn. He calls flop with lots more than just Ax I'd imagine. Lots of insiders, and weak second pairs that can't handle more pressure.

[Parasurama]

I'd shove river, he has a potsize bet left. After he c/r you on the turn his range is very polarized to nonsense that won't call the size of bet you made, or strong hands that will call a potsize bet anyhow.

I'm always double barreling this turn. He calls flop with lots more than just Ax I'd imagine. Lots of insiders, and weak second pairs that can't handle more pressure.

Very good point. I guess I didn't put him in because the river check made me think he didn't have that strong of a hand, but you're right his range is very polarized.

[Alexos]

any time a backdoor flush comes in and you have 1 to 2 PSB left just shove.