I agree with you that giving a free card here isn't as bad as a lot of people think. I actually take this line with overpairs/TPTK in some cases. But I don't think it's certain that Villain puts you on an overpair here. It's very possible that he calls a flop c-bet with a lower pair which he thinks is good. For pot control I would check behind on turn instead (obv. not this turn).