"upper reaches of a profession or pursuit," by 1909 in vaudeville slang. As an adjective by 1915. The same phrase was common in colloquial use late 19c.-early 20c. in a broad range of senses: "party, shindig, fun, frolic."
Big Brother
big deal
Big Dipper
Big Mac
big shot
big time
bigamist
bigamous
bigamy
bigass
big-boned