Just found a two headed quarter. Is it fake?

why would it be odd ?
I find it odd, unless you know exactly how and why it was made.
Maybe make your own thread, show pictures and provide weights of both halves, even though it really doesn't matter as it shouldn't weight exactly as a new one unless the person making it wanted it to weigh the same.

 

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If it has a seam, it's a magicians coin, made as a novelty after it left the mint. Weight is irrelevant. The tolerance of a quarter is 5.67 grams +/- 0227. Your quarters could have started on the heavy end and it would have been perfectly normal. The seam is the giveaway.

 

Wouldn't it be impossible for this to happen to a coin at the mint, given the machinery and process?

 

Yes.
A two headed quarter is done a some time. It can weigh some amount more or less than a normal quarter. It can have two heads or two tails or one of each. Totally depends upon the person making it decides.
(125) Making a Two-headed Coin - YouTube