Green’s Dictionary of Slang

1. an important person; thus big-league v., to associate with important people.

1914		Goodwin’s Wkly (Salt Lake City, UT) 25 Apr. 11/2: The big leaguer among the ladies was Mignon Heywood as Elizabeth [...] who was a veritable scream. She is a natural comedian.
1917		R. Lardner ‘Three Kings and a Pair’ in Gullible’s Travels 63: If Bishop’s friends sees him with Bessie they’ll say: ‘My! he’s copped out a bigleaguer.’.
1920		H.C. Witwer Kid Scanlon 64: All the big leaguers own their own tourin’ cars.
1946		M. Allen in W. Winchell 4 May [synd. col.] Well, Walter Winchell is a big-leaguer in every respect.
1999		Eble Campus Sl. Nov. 2: big league – socialize with rich or important people. ‘You’re just big-leaguing.’.

2. an important thing.

1928

J. Callahan Man’s Grim Justice 286: I decided to play the small [magazines] and thus write myself up to the big leaguers.

3. a resourceful person who can handle any situation.

1956

‘Toney Betts’ Across the Board 111: He was a big-leaguer who could not forget that he once had been broke.

4. a major criminal.

1955

‘Blackie’ Audett Rap Sheet 84: Later, I worked pretty close with Eddie when he was calling the shots for Johnny Dilllinger, Homer Van Meter and some of them other big leaguers I got tied up with in the 1930’s.