Green’s Dictionary of Slang

a promotion of, a reference to.

1995		L. Stavsky et al. A2Z 7/1: big ups – public acknowledgements for creative help or greetings given by a rapper at the mike or in a recording: MC Lyte freestyled a few minutes of big ups.
1998		Source Nov. 144: The trio was renamed The Fugees as a big-up to Clef and Pras’ Haitian roots.
2006		G. Malkani Londonstani (2007) 82: Extra blessings an big-ups would be going out to her tonite.