Green’s Dictionary of Slang

1. a sneak thief, esp. one who specializes in entering houses (occas. shops) and taking furs, cloaks and coats.

1663		Wandring-Whores Complaint title: A full discovery of the whole Trade of [...] Bawds, Whores, Fyles, Culls, Mobs, Budges, Shop-lifts, Glasiers, Mills, Bulkers, [...] and all other Artists, who are, and have been, Students of Whittington Colledge.
1665		Head Eng. Rogue I 48: Budge, One that steals Cloaks.
1671		‘L.B.’ New Academy of Complements 204: The seventh is a Budge, to track up the stairs.
1674		C. Cotton Compleat Gamester 6: Shoals of Huffs, Hectors, Setters, Gilts, Pads, Biters, Divers, Lifters, Filers, Budgies, Droppers, Crossbyters, etc., and these may all pass under the general and common appellation of Rooks.
c.1698		B.E. Dict. Canting Crew n.p.: Budge, c. one that slips into an House in the Dark, and taketh Cloaks, Coats, or what comes next to hand, marching off with them.
1712		‘Black Procession’ in Farmer Musa Pedestris (1896) 38: The sixth is a file-cly that not one cully spares, / The seventh a budge to track softly upstairs.
1725		New Canting Dict. n.p.: budge, One that slips into an House in the dark, and taketh Cloaks, Coats, or what comes next to Hand, marching off with them. If he meets with any body, who demands his Business, he asks, If such a Gentlewoman or Woman be within; and if he is told, They know not such Person, he begs Pardon, and says, He was mistaken in the House, and will not stay for a Reply.
1727		J. Gay Beggar’s Opera II i: Matt of the Mint, Ben Budge, and the rest of the Gang.
1737, 1759, 1760, 1776		Bailey Universal Etym. Eng. Dict. [as cit. 1725].
1754		Scoundrel’s Dict. 29: The Budge, who makes it his business to run into Houses, and take what comes first to hand.
1785, 1788, 1796		Grose Classical Dict. of the Vulgar Tongue.
1811		Lex. Balatronicum.
1859		Matsell Vocabulum 15: budge. A thief that sneaks into a store, and hides until the persons who lock up are gone, when he lets in his accomplice.
1869		‘Thief-Catcher’s Prophecy’ in W.H. Logan Pedlar’s Pack of Ballads 143: [as cit. 1712].
1889–90		Barrère & Leland Dict. of Sl., Jargon and Cant.
1890–1904		Farmer & Henley Sl. and Its Analogues.
1895		Crowe Aus. Sl. Dict. 12: Budge, a thief hiding in a house, so as to admit his brother thieves in the night.

2. the criminal speciality of sneak-thieving.

1676		A Newgate ex-prisoner A Warning for House-Keepers 5: The Budge it is a delicate trade, / And a delicate trade of fame.
1770		Proceedings Old Bailey 21 Feb. 142/1: He came home, and said he saw two lads about that he thought were going upon the budge [...] Going on the sneak, is to go into houses that are open to take things: going on the budge, is to burst the doors open.