Willie the Weeper is a tune from 1920, attributed to Walter Melrose, Grant Rymal and Marty Bloom. However, it was remarkably similar to Willie the Peeper, composed in 1912 by Harry Armstrong, Billy Clark and James Coogan, so we may consider it as largely plagiarised. This point was established by the great music researcher and sheet music collector Audrey VanDyke. (For a comparison of the two tunes, CLICK HERE.)
It's a tune every band should be able to play because it always goes well and because it has a number of interesting ingredients.
It consists of two themes of 16 bars each. The first is in a minor key. The second is in the related major. As for structures, the first theme may be considered as an 8 + 8, whereas the second is an AABA (four bars of each). On top of these features that give it the variety to make it interesting, Willie The Weeper is simply a jolly good tune. Below it is in D minor and F, but it goes well in other keys too, especially G minor and Bb. You may choose - as many bands do - to add a 4-bar Introduction and to play Theme B first. Most bands treat Theme B as the 'Chorus' and improvise on this part, which uses the simple Sweet Sue Progression (Dominant 7th to Tonic) three times, with an interesting 'Middle Four'.