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.

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.