Does Weird Al pay mechanical or other royalities?
He does a lot more than that. He gets specific permission from the artists, and does pay royalties. I'm not sure if the royalties are just the mechanical ones or if he pays more because he's got specific contracts with the original artists. It's not answered clearly in the FAQ on his site.

Incidentally, the friends I was mentioning who needed to get the mechanical rights... that was for a parody album, very much in the Weird Al vein.
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Tony Fabris