A new posting of another set of this song to the Forum reminds me that the links I gave here last year here need to be updated. I add only references to stable sites that take the trouble to acknowledge their sources, though it has to be said that some of the examples here at the Mudcat, referred to above, are given with no information at all as to what tune, if any, they might have been sung to, and no information at all as to where they might have come from.
At the Max Hunter Folk Song Collection (all with full texts, notation and sound files:
Little Billy As sung by Odis Bird in Marshall, Arkansas on August 6, 1958
Lovin' Polly As sung by Mrs. Allie Long Parker in Eureka Springs, AR on March 27, 1958
Willie Came Over The Main Wide Ocean As sung by Mr. Fred High in High, Arkansas on February 11, 1959
Pretty Polly As sung by Donia Cooper in West Fork, Arkansas on August 19,1959
At Lesley Nelson's Folk Music site:
The Outlandish Knight With tune; from Cecil Sharp's One Hundred English Folksongs. In that book (which was published as a resource for amateur and professional "art music" singers, not as a reference book), Sharp doesn't identify his source[s], saying only "I have recorded several fairly complete sets of words, from which that given in this book has been compiled." Elsewhere, however, he does name sources; the tune for this one came from Joseph Laver of Bridgwater, Somerset, in 1907, and the collated text is not significantly different from Mr. Laver's.
The Willow Tree (American Version) With tune; from The Colonial and Revolution Songbook (McNeil, 1996) : no prior source is quoted, though apparantly the authors believe their set to be 17th century American, which seems unlikely on the face of it.
Lady Isabel and the Elf-Knight Child's versions A-F. (Texts only).
The new posting to the Forum is The False Young Sailor; So far, no source or tune has been mentioned, but perhaps we'll get those later.