Tough spot, but if i was the villain i wouldn't put you on A-K,K-K, Q-Q or K-Q Because i'd figure that you would check it to me OOP, espeically if your solid and not that AGG. Because obviously, you would have us both drawing dead, or very close to it. So i'd put you on J-J, AA, or maybe A-Qs. People tend to drop out of pots alot easier when a SS is allin and theres going to be a automatic showdown. So if you bet only 35$ into the pot, it would be enough to get the info you need without completely committing yourself. He's obviously not playing j-10, so your either drawing to 2 outs, our he's drawing almost dead. He pushs with the auto showdown on the horizion, your drawing to 2 outs, then you can toss it and see for sure if your right or if he's just an idiot. Plus the 35$ bet looks like you want a call, which is good for a fold on a scary board, epeically since your solid.

*EDIT* On second thought i'm not that sure actually, this might just be a Setup spot to lose with no shot a saving it, im curious what everyone else has to say.