This says

Often times, a court will apply the “likelihood of confusion” test to a parody case. Courts have noted that a successful parody will rarely be considered infringement because the ultimate object of a parody is to entertain and not confuse the listener or buyer. There is no perceived “threat of confusion” and it is unlikely that the original artist’s profits will be negatively impacted by Weird Al’s versions. Because of this, original recording artists are unlikely to have a cause of action against Mr. Yankovic.>

Despite the unlikelihood of litigation, Weird Al always obtains permission from the original artist. He has stated, ”I have a long-standing history of respecting artists' wishes. So if (the artist) himself were objecting, I wouldn't even offer my parody for free on my Web site.”

By obtaining official copyright permission from the artists, Weird Al’s attorneys negotiate royalties which vary from a flat fee buyout to royalty participation. Weird Al's financial success is likely responsible for the willingness of most copyright owners to grant him permission to parody their musical compositions. It as made it possible for Yankovic to bargain for a lucrative share in the copyright of the parody version of the song.

Curious how he doesn't get 100% royalties if the song is fair use.