Yankovic came up with the idea for Fat while watching the Bad music video, when he had an epiphany that a parody of that song titled Fat would be a good sequel to Eat It (a previous Weird Al Michael Jackson parody). As he watched the Bad video, he imagined an obese version of himself trying to get through the turnstiles on a subway, and resolved that he would do it.
When performing in concert, Yankovic wears a fat suit and a mask that makes his face appear fat. Due to undergoing laser vision correction surgery, he no longer needs to wear glasses, though he wears glasses with non-prescription plastic lenses in order to help hold on the mask.
Directed by Jay Levey, the video for "Fat" parodies various elements of the "Bad" video by Jackson; Yankovic was able to get permission from Michael Jackson to use the same subway set from "Bad" for the video. Jackson had built an exact replica of the original set for the movie Moonwalker to be used in the segment called "Badder", and before striking it, he offered to allow Yankovic to use it.