Looks like QQ or a big draw like JTc or QKc / AQc. He would raise sets, and two pairs on the flop presumably (unless he's really goofy), so they're the only hands I can see him having.

That said, its either check raise all in or fold. I actually think big draw is his most likely holding here so check raising big is 1000 times better than folding but since the stacks are so deep it lets him get away when he's drawing and stack you when he's not. I don't know what to do either, but I think calling here is pretty bad since he's likely pair + flush or straight + flush or already has you beat, but you don't really know what's a bad card for you on the river. Maybe my read is bad tho.