[37offsuit]

I think the turn is the key here. You know you are ahead but if you get called there are a lot of bad cards for you. Any diamond puts the three flush, the board pairing puts a possible boat and you don't much like a Q or a J either since it puts four to a straight. You're out of position. He bet 15 on the flop, you check raised to $150 and he called. That screams draw to me. If he had a set, he'd likely repop you, not just call.

The turn is where you need to force him into a difficult decision. If he is on a draw or pair plus draw, then he's calling $375 to win $1560 (he puts no more in if he misses and likely stacks you if he hits since he's got position).

I overbet here and take down a decent pot or give him really terrible odds while committing myself on the river or I check raise all in if he bets, and can get away from the hand if it goes South and he checks behind (meaning a diamond on the river).

The way you played it, I check fold the river. He has to be on a draw here and if you check and he bets, then he's not doing it with worse than a straight (so you can fold to his range, given that you're calling 750 to get back half the pot (about 600) some portion of the time and lose to the flush some other percentage of the time.

So to sum up, I like the turn overbet best, check raise all in or check-check and fold the river given that it's the J of diamonds.