[band of silk, strip of cloth], 1550s, "a band worn across the body or over the shoulders," probably from Old North French escarpe "sash, sling," which probably is identical with Old French escherpe "pilgrim's purse suspended from the neck," perhaps from Frankish *skirpja or some other Germanic source (compare Old Norse skreppa "small bag, wallet, satchel"), or from Medieval Latin scirpa "little bag woven of rushes," from Latin scirpus "rush, bulrush," which is of unknown origin [Klein].
It also is attested in early Modern English as scarp. OED points to "the change of the initial p into f after liquids". As a cold-weather covering of warm and soft material for the neck, by 1844. Plural scarfs began to yield to scarves early 18c., on model of half/halves, etc.
[connecting joint in carpentry, the ends being cut or notched so as to fit into each other], late 13c. (implied in scarf-nail), probably from a Scandinavian source, such as Old Norse skarfr "nail for fastening a joint; diagonally cut end of a board," Swedish skarf, Norwegian skarv, from Proto-Germanic *skarfaz, source also of Dutch scherf, Old English scearfe "a fragment, piece"(from PIE root *sker- (1) "to cut"). Also used as a verb, "unite by means of a scarf" (1620s). Also borrowed into Romanic (French écart, Spanish escarba).
"eat hastily," 1960, U.S. teen slang, originally a noun meaning "food, meal" (1932), perhaps imitative, or from nautical slang scoff "eat hastily or voraciously, devour" which is attested from 1846 (compare U.S. tramps slang scoffing "food, something to eat," 1907). This is said to be a variant of scaff (by 1797) in the same sense, and scaff (n.) "food, provisions" is attested from 1768, but the group is of obscure origin. Perhaps the word comes ultimately from some survival of Old English sceorfan "to gnaw, bite" (see scarf (n.2)). South African scoff (n.) is said to be a colloquial representation of Dutch schoft "quarter of a day," hence "each of the meals of a day." Related: Scarfed; scarfing.