Green’s Dictionary of Slang

(US) tipsy.

1906		Salt Lake City (UT) 30 Mar. 4/5: He has [...] a shine on [...] an edge on.
1931		A. Hardin ‘Volstead English’ in AS VII:2 88: Terms referring to the state of intoxication: [...] Verbs: Edged.
1941		M. Prenner ‘Drunk in Sl.’ in AS XVI:1 Jan. 70/1: edged. [...] has an edge.