Ok, let's make some assumptions.

First, let's assume that he knows you have an overpair and that he can get your whole stack in.

Second, let's assume that as you said, his chances of beating your single big pair on the flop is 1 in 12.

Third, let's assume you are betting 5xBB preflop.

11/12 times, he loses 5xBB, or 55BB.

If your stack is LARGER than 55BB, he can call in this situation and be profitable over time.

Edit: obviously your stack needs to have his covered in this situation.