Green’s Dictionary of Slang

1. (US black, also drape down) to dress (up).

1936		A.E. Duckett ‘Truckin ’round Brooklyn’ in N.Y. Age 8 Feb. 7/1: Harry Richman of the town, who has a ‘rep’ for draping down.
1942		‘Digg Mee’ ‘Observation Post’ in N.Y. Age 29 Aug. 9/6: Harlem [...] is dead and still. Stachin’ and drapin’ isn’t the same upon ‘sugar hill’.
1953		L. Durst Jives of Dr. Hepcat (1989) 1: Let all the ickies drape in shape and fall from the pad hip to the tip and most mad.
1992		Dr Dre ‘Bitches Ain’t Shit’ 🎵 Snoop we got news / Your girl was trickin while you was draped in your county blues’.

2. (W.I.) to grab someone around the waist and aggressively lift them up.

1995

Francis-Jackson Official Dancehall Dict. 15: Drape the act of grabbing someone in the waist and hoisting him onto his toes: u, drape de bwoy.