"backside foremost," 1530s, probably a reduplication of arse, perhaps with suggestions of reverse.
Entries linking to arsy-versy
arse n.
"buttocks, hinder part of an animal," Old English ærs "tail, rump," from Proto-Germanic *arsoz (source also of Old Saxon, Old High German, Old Norse ars, Middle Dutch ærs, German Arsch "buttock"), from PIE root *ors- "buttock, backside" (source also of Greek orros "tail, rump, base of the spine," Hittite arrash, Armenian or "buttock," Old Irish err "tail").
To hang the arse "be reluctant or tardy" is from 1630s. Middle English had arse-winning "money obtained by prostitution" (late 14c.). To turn arse over tip is attested by 1884, along with the alternative arse over tit.
Every scrap of Latin Lord Edgecumbe heard at the Encaenia at Oxford he translated ridiculously; one of the themes was Ars Musica : he Englished it Bumfiddle. [Horace Walpole to the Countess of Upper Ossory, Aug. 9, 1773]
reverse adj.
c. 1300, "opposite, contrary in position or direction, turned backward," from Old French revers "reverse, cross, opposite" (13c.) and directly from Latin reversus, past participle of revertere "turn back, turn about, come back, return" (see revert). In reference to a gear mechanism enabling a vehicle to go backward without changing the rotation of the engine, by 1875. Reverse angle (shot, etc.) in film-making is from 1934. Reverse discrimination is attested from 1962, American English. Reverse dictionary, one in which the words are arranged alphabetically by last letter to first, is by 1954.
higgledy-piggledy
"confusedly, hurriedly," 1590s, a "vocal gesture" [OED] probably formed from pig and the animal's suggestions of mess and disorder. Reduplications in the h-/p- pattern are common (as in hanky-panky, hocus-pocus, hinch(y)-pinch(y), an obsolete children's game, attested from c. 1600).
Edward Moor, "Suffolk Words and Phrases" (London, 1823), quotes a list of "conceited rhyming words or reduplications" from the 1768 edition of John Ray's "Collection of English Words Not Generally Used," all said to "signify any confusion or mixture;" the list has higgledy-piggledy, hurly-burly, hodge-podge, mingle-mangle, arsy-versy, kim-kam, hub-bub, crawly-mauly, and hab-nab. "To which he might have added," Moor writes, crincum-crankum, crinkle-crankle, flim-flam, fiddle-faddle, gibble-gabble, harum-scarum, helter-skelter, hiccup-suickup, hocus-pocus, hotch-potch, hugger-mugger, humdrum, hum-strum, hurry-scurry, jibber-jabber, prittle-prattle, shilly-shally, tittle-tattle, and topsy-turvy. Many of these date to the 16th century. Miss Burney (1778) has skimper-scamper "in hurry and confusion."