On the flop, I don't see how you can't raise in this position, I certainly wouldn't feel like losing to a 6 outer, which is highly probable he has. Because you only called on the flop, now that you hit your 2nd pair, you don't even know if your hand is good or not, and raising here will certainly put you too deep into the pot to fold it, potentially if he does have the nut hand or case straight cards.