Oh that's a tough one. There's no way that I would have folded that on the turn. But whether it's a sound call mathematically, I'll leave it to others to respond .
If I bet as a bluff, I should be thinking "am I getting better hands to fold? Is it likely that he will fold x% of the time to a y sized bet to make it +EV?". If I bet for value, I should be thinking "am I getting worst hands to call? Am I ahead of enough of his range that this is a good value bet?".