"alcoholic drink," by 1821, perhaps 1714; probably originally a verb, "to drink a lot" (1768), variant of bouse (c. 1300), from Middle Dutch busen "to drink heavily," related to Middle High German bus (intransitive) "to swell, inflate," which is of unknown origin.
The noun was perhaps reinforced by 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.