bulge: [13] Etymologically, bulge and budget are the same word, and indeed when English first acquired bulge it was as a noun, with, like budget, the sense ‘pouch’. It came from Old French bouge ‘leather bag’, a descendant of Latin bulga, which may have been of Gaulish origin (medieval Irish bolg ‘bag’ has been compared). The word’s present-day connotations of ‘swelling’ and ‘protruding’ presumably go back to an early association of ‘pouches’ with ‘swelling up when filled’ (compare the case of bellows and belly, which originally meant ‘bag’, and came from a source which meant ‘swell’), but curiously, apart from an isolated instance around 1400 when bulge is used for a ‘hump on someone’s back’, there is no evidence for this meaning in English before the 17th century.
Additionally, from the 17th to the 19th centuries bulge was used for the ‘bottom of a ship’s hull’; it has now been superseded in this sense by bilge [15], which may well be a variant form. => bilge, budget
bulge (n.)
c. 1200, "wallet, leather bag," from Old French bouge, boulge "wallet, pouch, leather bag," or directly from Latin bulga "leather sack" (see budget (n.)). Sense of "a swelling" is first recorded 1620s. Bilge (q.v.) might be a nautical variant.