1570s, "swallow liquid greedily" (intransitive), 1580s in transitive sense, probably related to Old French gosillier "to go down the gullet; to vomit, chatter, talk," from gosier (13c.) "jaws, throat, gullet." Or imitative of the sound of drinking greedily. Related: Guzzled; guzzling.
1590s, "a drain," from guzzle (v.). From 1704 as "liquor," 1836 as "bout of heavy drinking."