The name "Willie," and the general theme, may (speculation here) have been inspired by the Stephen Collins Foster song, "Willie, We have Missed You," 1854. In turn, it inspired "Willie's Welcome Home- an Answer to Willie, We Have Missed You," words by A. Fleetwood, music by A. Von Smit, 1856.
Foster himself killed Willie in "Our Willie Dear is Dying," 1961.
These may be found at the Levy site. (Song not really tied to the others)