Not too many reads on villain. This is a zoom table, his hud is showing 33/4 over 24 hands, so quite likely a more passive player.

Seems like a pretty straightforward flat vs a presumably tight opening range.

Again seems like a standard peel, can't see any value in raising our dry straight here.

When he pots the turn, his hand looks a lot like JT, maybe a set with a flushdraw. Again I don't see much value in raising given we are in position. If a heart, a club or a board pair hits, he has to act first, so we will more information about his range when we have to act, possibly turning our hand into a bluff.

So he checks the flushing river, this card is interesting because neither of us could have had the NFD at any point. In a sense it makes it harder for us to rep this card with a bet. There's a good chance we would have raised JT with Khh or Qhh at some point. And hands like KJhh aren't really strong enough to call 2 pot sized bets. With no heart in our hand, together with the fact that we have reverse blockers (we block 2 non heart tens), this must be a check if we're playing a balanced, reasonable strategy.

However, I don't think this guy is hand reading at all. Should I go for it and try to make him fold JT? or is he too likely to call with that, and will have some T/J high flushes that are pot controlling?