c. 1200, "a wallet, leather bag," from Old French bouge, boulge "wallet, pouch, leather bag," or directly from Latin bulga "leather sack," from PIE *bhelgh- "to swell," extended form of root *bhel- (2) "to blow, swell." Sense of "a swelling, a rounded protuberance" is first recorded 1620s. Bilge (q.v.) might be a nautical variant. Meaning "bulging part of a military front" is from 1916.

early 15c., bouget, "leather pouch, small bag or sack," from Old French bougette, diminutive of bouge "leather bag, wallet, pouch," from Latin bulga "leather bag," a word of Gaulish origin (compare Old Irish bolg "bag," Breton bolc'h "flax pod"), from PIE *bhelgh- "to swell," extended form of root *bhel- (2) "to blow, swell."

The modern financial meaning "statement of probable expenditures and revenues" (1733) is from the notion of the treasury minister keeping his fiscal plans in a wallet. Also used from late 16c. in a general sense of "a stock, store, or collection of miscellaneous items," which led to 18c. transferred sense "bundle of news," hence the use of the word as the title of some newspapers.

1838, "small bag, usually embroidered or otherwise ornamented, containing perfume powder, etc., placed among articles of dress," from French sachet, literally "little sack" (12c.), a diminutive of sac (see sac). A reborrowing of a word that Middle English had used in the sense "small bag, wallet" (15c., saket).

"post, letters," c. 1200, "a traveling bag, sack for keeping small articles of personal property," a sense now obsolete, from Old French male "wallet, bag, bundle," from Frankish *malha or some other Germanic source, from Proto-Germanic *malho- (source also of Old High German malaha "wallet, bag," Middle Dutch male "bag"), from PIE *molko- "skin, bag."

The sense was extended to "bag full of letters" (1650s; perhaps via phrases such as a mail of letters, 1654) and "person or vehicle that carries postal matter" (1650s). From thence, to "letters and parcels" generally (1680s) and "the system of transmission by public post" (1690s).

As a newspaper name, by 1789. In 19c. England, mail was letters going abroad, while home dispatches were post. Sense of "a personal batch of letters" is from 1844, originally American English. Mail slot "narrow opening in an exterior door of a building to receive mail delivery" is by 1893, American English. OED defines it as a "letter-slit."

[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.