Green’s Dictionary of Slang

1. (US drugs) a (half-smoked) marijuana cigarette.

1949		Monteleone Criminal Sl. (rev. edn) 39: burnie Marihuana cigarette.
1952		Lannoy & Masterson ‘Teen-age Hophead Jargon’ AS XXVII:1 24: BURNIE, n. Half-smoked marijuana cigarette [LAPD].
1960, 1975		Wentworth & Flexner DAS.
2001		ONDCP Street Terms 4: Burnie — Marijuana.

2. (US juv.) a pre-adolescent who smokes, drinks and uses drugs.

1987

G.A. Fine With the Boys 182: At one school in Bolton Park, kids are classified as to whether they are daredevils (kids who get into trouble), jocks, or burnies (burn-outs – preadolescents who smoke, drink, and use drugs).