Green’s Dictionary of Slang

1. (US) self-important.

1969		P. Roth Portnoy’s Complaint (1969) 158: All your big words and big shit holy ideals.
1975		J. Carr Bad (1995) 118: He took red devils and thought he was big shit.

2. (US black) important.

2008

‘Grandmaster Flash’ Adventures 140: Hank’s fronting like he's big shit, but everybody on the street knows he stole his rhymes. Hank ain’t the real.