Small pair, common situation

[NMcNasty]

You are in one of the blinds with a small pocket pair. Either the button or cutoff raises preflop and you call. Assume your opponent is an average winning aggressive player, but aside from knowing that you have no reads on him or her. The flop comes down paired and over your cards. For example if you have 44, the flop comes down 966.

What exactly is the best line to take here? Your hand is good on the flop a good majority of the time, but even with garbage your opponent has a ton of outs and there are a ton of turn cards he can bluff on. I just can't see how check-calling can be profitable even though it intuitively seems standard. Check raising seems a bit expensive and puts you at a loss on what to do on the turn, and betting out is certainly a possibility but just seems a little weak. Is check-folding a possibility? As sick as it sounds I think it might be, it just seems ridiculous to fold when you know you're ahead around 75% of the time on the flop. Its just when you're up against a player capable of firing one or two more barrels, there really aren't a lot of turn and river combinations you can be happy with.