Green’s Dictionary of Slang

budge n.1

also budgie
[SE budge, a kind of fur, consisting of lamb’s skin with the wool dressed outwards]

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

[UK]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.
[Ire]Head Eng. Rogue I 48: Budge, One that steals Cloaks.
[UK]‘L.B.’ New Academy of Complements 204: The seventh is a Budge, to track up the stairs.
[UK]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.
[UK]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.
[UK]‘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.
[UK]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.
[UK]J. Gay Beggar’s Opera II i: Matt of the Mint, Ben Budge, and the rest of the Gang.
[UK]Bailey Universal Etym. Eng. Dict. [as cit. 1725].
[UK]Scoundrel’s Dict. 29: The Budge, who makes it his business to run into Houses, and take what comes first to hand.
[UK]Grose Classical Dict. of the Vulgar Tongue.
[UK]Lex. Balatronicum.
[US]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.
[UK] ‘Thief-Catcher’s Prophecy’ in W.H. Logan Pedlar’s Pack of Ballads 143: [as cit. 1712].
[UK]Barrère & Leland Dict. of Sl., Jargon and Cant.
[UK]Farmer & Henley Sl. and Its Analogues.
[Aus]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.

[UK]A Newgate ex-prisoner A Warning for House-Keepers 5: The Budge it is a delicate trade, / And a delicate trade of fame.
[UK]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.

In compounds

budge and snudge (n.) [snudge n.; note the 1950s British TV sit-com Bootsie and Snudge, based on the misadventures of two army friends]

(UK Und.) a housebreaker and their accomplice.

[UK]Hue and Cry after Mercurius Democritus 8: The number of vicious Artists are unknown to the Mrs [i.e. Masters] and the Wardens of their own fencing Mobs [...] the life of which Company are High-way Pads, Glasiers, Shop-lifts, Fob-sylers [sic], instead of Bung -Tipers [sic] Bulkers, and some for the Mill, Budg and Snug.
[UK]A Newgate ex-prisoner A Warning for House-Keepers 5: A Budge and Snudge commonly go together, a Budge is one that goes loytering down the street, till he can find somebodies door open [...] if there be nobody in the house, then they are so bold to take what stands next them and gives it to his Snudge, who snudges away with it to his fencing cins [sic] who buyes it.