Budge
late 16th century: from French bouger ‘to stir’, based on Latin bullire ‘to boil’.
wiktionary
Borrowed from Middle French bougier, from Old French bougier, from Vulgar Latin *bullicāre(“to bubble; seethe; move; stir”), from Latin bullīre(“to boil; seethe; roil”).
From Middle English bouge, bougie, bugee, from Anglo-Norman bogé, from Anglo-Latin *bogea, bulgia, related to Latin bulga(“a leathern bag or knapsack”). Doublet of bulge.
etymonline
budge (v.)
1580s (intransitive) "to move, stir, change position, give way a little;" 1590s (transitive) "change the position of;" from French bougier "to move, stir" (Modern French bouger), from Vulgar Latin *bullicare "to bubble, boil" (hence, "to be in motion"), from Latin bullire "to boil" (see boil (v.)). Compare Spanish bullir "to move about, bustle;" Portuguese bulir "to move a thing from its place." In 16c. canting slang, "a general verb of action, usually stealthy action" (Farmer, "Musa Pedestris," who gives among his examples budge a beak "to give the constable the slip," budge out or off "to sneak off"). Related: Budged; budging.
