O.E. fyllan, from P.Gmc. *fullijan (cf. O.S. fulljan, O.N. fylla, O.Fris. fella, Du. vullen, Ger. füllen "to fill"), a derivative of adj. *fullaz "full." The related noun meaning "a full supply" is M.E. fille, from O.E. fylle. To fill the bill (1882) was originally U.S. theatrical slang, in reference to a star whose name would be the only one on a show's poster. Related: Filled; filling.
Complete by supplying required information, especially in writing. For example, Please fill out the application form, or I don't quite understand this drawing, so fill out the details.
[ Late 1800s
Become enlarged, distended, rounded in outline. For example, The wind filled out the sails, or He's put on weight and really filled out. Applied to objects, this expression dates from about 1700, but to persons or animals becoming fatter, only from the late 1800s.