river value thin? sizing?

[daven]

villain is 45-10 over 30, no reads postflop except he's folded a couple of flops
my image is pretty active i guess, i've been winning a few pots without showdown.

PokerStars No-Limit Hold'em, $0.50 BB (8 handed) - PokerStars Converter Tool from FlopTurnRiver.com

CO ($51.90)
Hero (Button) ($94.20)
SB ($53.25)
BB ($52.45)
UTG ($30.80)
UTG+1 ($19.50)
MP1 ($21.50)
MP2 ($62.70)

Preflop: Hero is Button with J, A
5 folds, Hero bets $1.25, SB calls $1, BB calls $0.75

Flop: ($3.75) A, 8, J (3 players)
SB checks, BB bets $1.50, Hero raises to $6.10, 1 fold, BB calls $4.60

Turn: ($15.95) 9 (2 players)
BB checks, Hero bets $15, BB calls $15

River: ($45.95) 2 (2 players)
BB checks, hero thinks a while, timer ticking...

[PKKFW]

I probably miss alot of value in situations like this so I'd love to hear others thoughts but I'd be checking behind.

Seems to me the villain could too easily have a flush or straight.

[rpm]

interesting spot you have there. i imagine i'm making a ton of mistakes in these kind of spots as well. i feel like we can vbet kind of small to get crying pot-odds calls from worse two pair hands or AQ/AT. but it really really sucks when we get bombed given how good our price will be. given he is pretty passive player OOP in a deep pot against a very strong line, i don't think hands like AJ/A9/A8 should be discounted (by him not 3betting flop or bombing the turn), and so are probably still in his range on the river.

let's look at some combos. of the range he gets to the river with, i would guess he calls a bet of up to $17 with:

we beat:
AJ - 4
A9 - 6
A8 - 6
J9 - 6
J8 - 6
AQ - 8
AT - 8
(44 combos)

beats us:
KhQh
KhTh
Kh9h
QhTh
Qh9h
Qh7h
Th9h
Th7h
Th6h
9h7h
9h6h
7h6h
7h5h
6h5h
6h4h
5h4h
4h3h
QT - 16

(34 combos)

so if we somehow knew that he never bombs us with worse (because he can "tell we're scared of the flush" or something) then i'm quite happy betting up to $17 and folding to a jam (if we pretend he never raises us, even with the nuts, then we have 56% against that continuing range as a whole). obviously our equity against his flatting range improves as we start removing nut hands (because they jam). for example, if we remove all Kxhh and Qxhh hands from his calling range, then we have 63%. i think that the EV lost the times (if ever) that he jams with worse will be outweighed by the fact that we probably have 65-70% against the range he flats with. so i'm going something in the vicinity of $15-18

sorry if that wording is a tad scat. i often have trouble explaining my thoughts when it comes down to really nit-picky combo-counting kind of hands. i guess i should also say that i, in no way, 100% advocate taking the above action as i am pretty unsure of how to proceed myself. the above is the best i could come up with and logic behind it.

edit: so i fucked up early in the process by giving him J9 (or J8, whichever makes two pair on the turn) which he probably doesn't have given that we raised the flop. this makes it somewhat closer than i thought. however i still don't think it would be a huge mistake to go somewhere between $15-18 and fold to a jam.