thin value bet with 2 pair on a 4 straight board?

[mcatdog]

I don't have any detailed reads because we'd been playing 3-handed vs a fish but he just left and this is the first hand of heads-up. All I know is villain is on the tight side and I don't think he's particularly tricky, but I'm sure he's at least decent at poker. Should I value bet the river and what's the best bet size?

PokerStars Pot-Limit Hold'em, $6 BB (2 handed) Poker-Stars Converter Tool from FlopTurnRiver.com (Format: FlopTurnRiver)

Hero ($669.55)
BB ($623)

Preflop: Hero is Button with J, K.
Hero raises to $17.95, BB calls $11.95.

Flop: ($35.90) T, 2, A (2 players)
BB checks, Hero bets $24, BB calls $24.

Turn: ($83.90) K (2 players)
BB checks, Hero checks.

River: ($83.90) J (2 players)
BB checks, Hero...

[ATOTHEC101]

68 on river as theres a ton of rag aces in his range as well as k10 and j10. Due to his passive line and the fact its hu i think youll get value from these hands, if you check your losing value fo sho.

[IowaSkinsFan]

ofc bet, you could do something gay like 25 or 3/4ths pot.