I'd bet the turn it would really piss me off to let a free diamond fall should he happen to have a random one in his hand. Or give him a free shot at a 6 outer (or 10 outer as he had here).

Usually at these levels nobody is going to CR bluff/semi-bluff you there unless they're a batshit crazy maniac. 2 pair is gonna CR there and depending on the player a made flush will either CR there or try to pull it off on the river sometimes because it looks cool.

So I like betting the turn then check behind on the river if you're concerned or the board gets scary.