Weird Al's "Word Crimes" is a parody of Robin Thicke's "Blurred Lines." Al gets permission from original artists to maintain good relations with the industry - but even if he hadn't, this usage would almost certainly be protected under Fair Use, since it is a parody.
But the complication is that Marvin Gaye's estate sued Robin Thicke, and the jury found that "Blurred Lines" did indeed constitute infringement of "Got To Give It Up."
What I have never heard anything about, though, is what this means for Weird Al. Could Marvin Gaye's estate sue Al directly, or does the parody defense still work even though it is a parody of a knockoff? Would Marvin Gaye's estate just get a portion of whatever deal Al made with Robin Thicke?
I know there is a previous question about a parody of a parody, but that is a different situation.