A big blind is normally referred to as a "small bet" (SB) and is half a big bet (BB).

You haven't said what limit you are playing.
If there are indeed only 2 "big blinds" in the pot, apart from being a very tight game, he must have been on the small blind and you on the big blind.

If so, he could have virtually anything. It is difficult to know the best play without a read on the opponent. I like a raise here. If he is passive he might check the turn.