Green’s Dictionary of Slang

1. (US prison) to eat prison food.

1723		C. Walker Authentick Memoirs of Sally Salisbury 90: There is scarce a Jayl in Town, but what I have made a present of a Member or two [...] where I have sent some Stripp’d Lover a Grazing.
1918		H. Simon ‘Prison Dict.’ in AS VIII:3 (1933) 27/2: GRAZE. Go to mess.
1950		Goldin et al. DAUL 86/1: Graze. (mid-West and scattered areas) To eat at the general prison mess or main line.

2. to eat; thus grazing n.

1913		H.G. Van Campen ‘Life on Broadway’ in McClure’s Mag. Mar. 38/1: He asked me to graze at Rector’s.
1945		F.H. Hubbard Railroad Avenue 345: Grazing Ticket – Meal book.
1987		Eble Campus Sl. Oct. 5: scarf [...] Also graze.
1996		CyberBraai Lex. at www.matriots.com 🌐 To graze means to eat. If you are invited to a bioscope show, you may be told: ‘We’ll graze first – and then hit the flicks.’.
1999		Guardian G2 25 June 7: The Americanised way of grazing creeping in here is terribly sad.