Green’s Dictionary of Slang

piece v.

In phrases

piece off (v.)

(US) to hand over a large sum of money which will then be returned in smaller portions.

H.B. Darrach Jr. ‘Sticktown Nocturne’ in Baltimore Sun (MD) 12 Aug. A-1/2: Rooms upstairs, rents them to Jacks. Hit the beach, maybe thousand [...] of cabbage, piece it off to Fanny, get it back fifty, hundred at a time .