Budget
late Middle English: from Old French bougette, diminutive of bouge ‘leather bag’, from Latin bulga ‘leather bag, knapsack’, of Gaulish origin. Compare with bulge. The word originally meant a pouch or wallet, and later its contents. In the mid 18th century, the Chancellor of the Exchequer, in presenting his annual statement, was said ‘to open the budget’. In the late 19th century the use of the term was extended from governmental to other finances.
wiktionary
Recorded since 1432 as Middle English bogett, bouget, bowgette(“leather pouch”), borrowed from Old French bougette, the diminutive of bouge(“leather bag, wallet”) (also the root of bulge), itself from Late Latin bulga(“leather bag, bellow”), of Gaulish origin (Celtic, compare Old Irish bolg(“bag”), Breton bolc’h(“flax pod”)), a common root with the Germanic family (compare Dutch balg(“bellows”)), from the Proto-Indo-European *bʰelǵʰ-. More at belly.
etymonline
budget (n.)
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.
budget (v.)
"to include in a (fiscal) budget," 1884, from budget (n.). Related: Budgeted; budgeting.