What are you planning on doing on the turn? Any broadway card & spade is bad, and its unlikely he's going to just quit bluffing.
I'd really like this more if you were in position, since it'd be a million times easier to get a cheap showdown. Also, you were barely getting set mining odds
preflop... I guess that's why you're contemplating floating him.
I think I'd like check/raising, since we're OOP and so many turn cards will absolutely suck. Plus he's drawing somewhat live with most of his hands having overcards. The only thing that worries me is that he c-bet for full pot, but in my experience that's kinda bluff, especially if your site has a bet pot button & he hits it fast. Generally big hands put more thought into their bets than just "I HAZ BIG HAND, MASH BET POT BUTTON!"