"alcoholic drink," by 1570s, also bouze (rhyming with carouse in poetry), also as a verb, probably a variant of Middle English bous "intoxicating drink," (mid-14c.), which is from Middle Dutch buse "drinking vessel" (also as a verb, busen "to drink heavily"), which is related to Middle High German bus (intransitive) "to swell, inflate," which is of unknown origin.
Mostly a cant word late 18c. The noun use and the -z- spelling (1830s) might have been popularized partly by the coincidental name of mid-19c. Philadelphia distiller E.G. Booz. Johnson's dictionary has rambooze "A drink made of wine, ale, eggs and sugar in winter time; or of wine, milk, sugar and rose-water in the summer time." In New Zealand from c. World War II, a drinking binge was a boozeroo.