Loose passive/nitty table overall with the exception of the villain in this hand who seems to be surprisingly competent for a 1/2 game. He's been playing mostly TAG while still loosening up in LP, successfully value betting thin, hasn't really gotten to showdown without the goods. Hero is effective stack at ~$720. OTTH

Folds around to hero
Hero (MP) raises to 10 with KJ
Villain (button) calls

Flop (21) K J 9
Hero bets 10
Button calls

Turn (39) 4
Hero bets 30
Button raises to 60
Hero calls

River (159) 3
Hero checks
Button bets 120
Hero ??

Similar story to the other hand. I prefer stronger PSB on flop given wet board texture and V's likely pre-flop button flatting range as you describe V.

Would V raise turn with made flush? Yes, if it's a small flush vulnerable to your MP raising range which contains plenty of overcard hearts. H also cannot rule out V's raising QT to protect his straight against H's overcard hearts (especially H's AQ combos with a heart also picking up a gutshot draw) and possibly against H's KJ combos too. He could have 99 also, but I expect he would have reraised pre-flop on button with this.

AP, I can find a river fold based on the action. Occasionally I expect V to show up with KJ here too. More often than not I expect to see a small flush or QT.

That said, I find post-flop bet sizing to be one of the hardest aspects of LLNLH, especially OOP. Only the very best players have mastered it. Your two posts illustrate this common and vexing problem very well.

The GTO school suggests that you don't want to scare away your customers too often with excessive post-flop bets. While this is true in theory, you also greatly complicate your decision-making process on later streets by under-betting a good flop, especially when playing OOP.

I suppose H's post-flop bet would have been fine with position, but OOP I prefer something bigger. I know this is an exploitable leak versus a very good player, but they are usually found at 2/5 where I venture only infrequently. I'm hoping some of the more experienced players here will weigh in on this interesting topic so I can learn from them.

Call turn, fold river.

I'm calling riv
Post sizing seems suspect this deep, and a lot of value hands should be raising flop or turn bigger.

Prob the nuts or air, don't think smaller flushes min click

Check the turn , may allow you to get to a cheaper river , maybe not , but generally not a great card for you, as played I probably nit fold without reads , unless villian is capable and you've seen him taken similar lines as bluffs, otherwise in most 1-2 games this line screams value , would he ever bet 2pair on this runout ?

Bet more OTF and waaaaay less OTT.

Your approach to sizing seems weird, bet sizing is complex but on the most basic level, you're trying to get people to pay the maximum amount with worse hands, which in turn is influenced by how good your hand is and how hard it is for them to call with worse. Here your hand gets significantly worse OTT and it becomes drastically harder for people to call, yet you size up.

I'm calling river, minraise lines are usually the nuts but this whole line is suspicious. The turn minraise would usually be specifically the nut flush, as the vast majority of players wouldn't let you draw that cheap if they had a non-nut flush. If V really had the NFD though, he might have chosen to raise the flop, as that's going to make your life pretty difficult if you have something like AK. He would probably also just raise larger OTT considering you're deep and he has the nuts. There's also a tension between his turn line, where he seems more interested in keeping you on the hook than getting max value, and his giant sizing OTR. I'm overall not buying the story he's telling me, basically.

If we're beaten I actually expect to see QT, which slowplayed flop because LDO, who doesn't love to slowplay, then wasn't sure what to do on such a wet turn and minraised, then is comfortable blasting river as it looks very unlikely you have a flush.