Green’s Dictionary of Slang

weary adj.

drunk.

1678		J. Ray Proverbs (2nd edn) 87: Proverbiall Periphrases of one drunk. He’s disguised [...] He is very weary.
1737		B. Franklin ‘Drinkers Dictionary’ in Pennsylvania Gazette 6 Jan. in AS XII:2 92: They come to be well understood to signify plainly that A MAN IS DRUNK. [...] He’s very Weary.
1890–1904		Farmer & Henley Sl. and Its Analogues.