IIRC Weird Al treats his parodies more like covers (even going so far as to get permission), and there are credits for the composers, etc. So I wouldn't be surprised if they pay out more like covers than parodies.
He likely doesn't want to be in front of the Supreme Court someday having to defend the parodic aspect like the famous Barbie Girl case, especially as it is not clear that all of his songs are parodies of the song and not some other aspect in the format of the song.
He likely doesn't want to be in front of the Supreme Court someday having to defend the parodic aspect like the famous Barbie Girl case, especially as it is not clear that all of his songs are parodies of the song and not some other aspect in the format of the song.