Talk about time travel- answering a question five years old!
Budget, meaning a pouch, bag or wallet is the first meaning given in the Oxford English Dictionary. Meaning number two is a leather or skin bottle. Number 3 is a bundle, or the contents of a wallet.
Not until they get to 4 do we find our usual meaning, a statement of revenue and expenditure.
A budget is also a leather socket for retaining the butt of a cavalry carbine.