Confuzzled on River

[FGators]

I don't have ptracker running because it froze my computer but I imagine villain is in the 30/15 range. He sees a lot of flops and is at least reads 2+2 because he asked me at the table if I'm "the real FGators". lol. Anyway, what do you think I should do on the river?

We both have over $400, FWIW.

Hero raises to $8 on button with 108spades. BB calls

Flop: 10 8 7 rainbow
BB checks, Hero bets $12, BB calls

Turn: K no flush
BB checks, hero bets $38, BB calls

River: 7
BB checks, hero?