This would be the case EXCEPT Two Face uses a double sided silver dollar rather than a regular one with one side that's anything between visibly scratched or charred so his coin does have a 50/50 chance of landing on either side rather than the 49/51 chance.
I don't know, dude. It seems to me that nothing would alter the weight of a coin too much, within the parameters of what we're talking about. My impression of the study was more that it had to do with starting position than weight. The results didn't indicate that the "heavy" side or the "light" side wound up showing more often, just that whichever side it began in was more likely to be the outcome. This somewhat indicates that the "weight" of the sides is irrelevant. There's just something about the mechanics of throwing that means it's very slightly more likely that the coin will return to its starting position. That's how I took it, anyway.