Preflop
Like in the K9 hand this spot is pretty marginal, and folding would not be insane. You can also stick in a call, since it was after all a CO open. And finally you can 3-bet, but suited
hands are preferred for 3-betting, because they have more
equity and playability when called. More importantly though a 3-bet need to be much larger. When you are giving him better than 3:1 plus position on you, he is never going to fold anything. The standard sizing here is 60c, and you only made it 30c, so this is a pretty significant mistake.
Flop
Standard C-bet and not going to discuss the sizing, because I dont think, its all that important.
Turn
The A on the turn is the classic "scare card", which makes it easy to
bluff but difficult to bet for value. Sometimes he will have it, and then you are just value owning yourself, if you bet again. And at the same time its a scare card to many of those hands, you still beat. Like his 88-QQ, or his K9-KT. So I think, your hand is to in between to bet again.
River
As played I would definitely check and evaluate. He gave you a good price, but you only beat a bluff, and what is he even
bluffing with? There is a busted flushdraw, but the nut flushdraw is now top pair, and with you holding J of hearts, he cant have hands like QJ, JT or J9 of hearts either. You also lose to hands like AQ or AT, that might have floated the flop. Or for that matter some random 7X, if they stuck around. So even though I hate folding getting such a great price, I think, I let this one go.