Value bet this river or hope to check it down?

[pokernicus]

IMHO, you should value bet this river. I doubt your opponent would check raise the river here (especially since the turn got checked through). If you get a chance, please fix the hand so it's more clear what happened (rather than us having to rely on guesswork...) -- e.g., how could UTG fold the turn?

Judging from the little info I have, it smells like your opponent has a ten himself -- I can't imagine anyone with a set would check the turn with the straight and flush draws out there.