Green’s Dictionary of Slang

(US) important, substantial, powerful.

1909		Chickasha Dly Exp. (OK) 12 Aug. 4/3: When Noah Webster led the batting — He had these slangsters on the fuzz / When it came down to Big league chatting.
1914		F. Norris in Everybody’s mag 31 682/1: ‘Say, this is big-league stuff!’ called Sidwell from the easel. ‘Old Andrew has put it across and nailed it there, Fred. This stuff is ace.’.
1918		J.N. Hall High Adventure 58: Now don’t try to pull any big league stuff.
1923		H.C. Witwer Fighting Blood 8: You can tell a big league head soda jerk by the way he picks up a glass.
1933		N. Algren ‘So Help Me’ in Texas Stories (1995) 15: Guys like me can’t never get away with bull like that to big-league lawyers like yourself.
1943		I. Wolfert Tucker’ s People (1944) 113: They’d all think he was one hell of a real, regular big league son of a bitch.
1956		N. Algren Walk on the Wild Side 67: I’m a big-league kid from a big-league town.
1958		R. Prather Scrambled Yeggs 72: That’s big league. Not good to mess around with.
1963		H.S. Thompson letter 19 Nov. in Proud Highway (1997) 414: The Reporter is about the best magazine in the country [...] and as big-league as they come.
1973		G.V. Higgins Digger’s Game (1981) 110: After all these years, Greek and Bloom’re big league.
1986		S. King It (1987) 523: That was weird – I mean really big-league weird.
1995		J. Stahl Permanent Midnight 148: One of the less-known, wholly unexpected secrets of Big League Geeze-dom.