From the Super Mario Wiki
The Diet Book is a book found in Super Paper Mario. During Mario, Luigi and Bowser's visit to The Underwhere, they meet a hag named Hagra, who tells them that she loaned her Diet Book to a D-Man. She explains that she wants the book back, however she's too old to go get it herself, and sends the heroes to fetch it for her. The D-Man willingly gives up the book, stating the diet didn't work and was just a fad anyway. Upon the return of the Diet Book, Hagra rewards the heroes with a key that allows them to continue their progress through the Underwhere Road.