There are two sets of Back and Sides Go Bare in the DT; one from literary sources, the other from oral tradition.
LET YOUR BACK AND SIDES GO BARE With tune; Dick Greenhaus comments, "Popularized, as far as I know, by RAF pilots in WWII". The text is virtually the same as that noted by Cecil Sharp from Robert Parish of Exford, Somerset, in 1907, which he called The Beggar. It's not impossible that that may have been the original source of the set in the DT, though if it was, the tune has been changed a fair bit.
BACK AND SIDE GO BARE A book is cited as source, but no other information is given. There is a reference, however, to JOHN DORY, which is the tune used; that file refers to Chappell's Popular Music of the Olden Time (1859), which places Back and Sides (as I cannot eat but little meat) in the play Gammer Gurton's Needle (1575), though Chappell considered it older. He quotes only four of eight verses; the DT file has all eight, but apparantly in the wrong order. Chappell wrote:
"I CANNOT EAT BUT LITTLE MEAT. This song was sung "in a right pithy, pleasant, and merry comedy," called Gammer Gurton's Needle, which was printed in 1575, but the Rev. Alex Dyce has given a copy of double length from a manuscript in his possession, and "certainly of an earlier date than the play." It may be seen in his account of Skelton and his writings, vol. i., p.7... Warton calls it "the first drinking song of any merit in our language."
The tune is printed in Stafford Smith's Musica Antiqua, and in Ritson's English Songs. Ritson says: "Set, four parts in one, by Mr. Walker, before the year 1600." And Smith, not knowing, I suppose, who Mr. Walker was, seems to have guessed Weelkes; but it is the old tune of John Dory in common time."
Claude M. Simpson (The British Broadside Ballad and Its Music, 1966) adds:
"The famous drinking song in William Stevenson's Gammer Gurton's Needle, I can not eate but lytle meate, has been set as a four-part round to a common-time version of John Dory, but on what authority remains a mystery."