Green’s Dictionary of Slang

1. a nickname for a very thin person; thus matchstick with the wood shaved off, an exceptionally thin person.

1959

I. & P. Opie Lore and Lang. of Schoolchildren (1977) 189: He’s as fat as a matchstick with the wood shaved off. [...] Thin people inspire almost as many names [...] matchstick (sometimes abbreviated to ‘matchy’).

2. (N.Z. prison, also match) a very thin marijuana cigarette.

2001

D. Looser Boobslang [U. Canterbury D.Phil. thesis] 115/1: matchstick (also match) n. a very thin­ rolled cigarette containing marijuana.