OK, let's go back to your initial read. You figured he had "Any pair, any 2 big cards". Probably a decent read. If you are right - what do you beat with that flop?
Any pair? - you have 6 outs - yech
AK? - your dominated - yech
AQ? - split
AJ? - chit, your dead
KQ? - wouldn't that be nice
KJ? - oops

If you trust your read then you have to lay it down on the flop.

With that weak flop bet, the other question is - Did he call with a 87s type hand? If you have seen him do this and are convinced that is what he has done then push. At this stage of the SnG, if I am in a raised pot, I have to be willing to play for my stack.