Green’s Dictionary of Slang

1. squinting; also as adv. (see cit. 1938).

1837		‘Old Hat’s The Very Thing We Like’ in Ticklish Minstrel 29: There’s boss-eyed Peg.
1851		‘Epistle from Joe Muggins’s Dog’ in Era (London) 21 Sept. 5/1: That boss-eyed young Forrester.
1860		Hotten Dict. of Modern Sl. etc. (2nd edn) 102: BOSS-EYED, a person with one eye, or rather with one eye injured.
1873		Sl. Dict.
1885		Bulletin (Sydney) 29 Aug. 12/4: He is now haunted in his business and his leisure hours by hair-lipped and fur-capped clients, who request (confidentially) to be ‘laid on.’ ‘If it’s as big as you pitch it is, Harry,’ said Boss-eyed Melchisedech, ‘you can bet the fust lot ain’t cleared out half the stuff.’.
1900		Marvel 21 Dec. 15: Mi boss is a bit boss-eyed.
1907		D. Stewart Shadows of the Night in Illus. Police News 31 Aug. 12/4: ‘That big, red-haired fellow is boss-eyed Bob Heffer’.
1914		E. Pugh Cockney At Home 253: He called me a boss-eyed bounder!
1916		Wipers Times 6 Mar. (2006) 29/2: Bertie, the boss-eyed boot boy.
1934		J. Franklyn This Gutter Life 149: ‘Who wants ’im? – who wants the boss-eyed sod?’ [...] ‘Don’t you call my bloke boss-eyed – you poxy mare!’.
1938		X. Herbert Capricornia (1939) 155: That ain’t dishonest — so you needn’t look boss-eyed at me.
1943		Radio Fun 10 July 13: I just feel in the empty hat and produce a beautiful boss-eyed bunny!
1958		A. Sillitoe Sat. Night and Sun. Morning 132: I’ll get some [glasses] some day. They wouldn’t suit me though. I’d look too much like a boss-eyed bookie.
1963		H.E. Bates Oh! To be in England (1985) 383: They were all going boss-eyed, watching telly.
1975		A. Bleasdale Scully 122: If it’s ‘no’ y’tell him he’s a boss-eyed bastard.
1999		Guardian Rev. 17 July 4: A rudimentary cartoon character. A little blob of orange coat and boss-eyed pain.
2001		OnLine Dict. of Playground Sl. 🌐 boss-eyed n. cross eyed.

2. tipsy, drunk.

1954

K. Williams Diaries 8 Sept. 104: I returned to Marchmont Street feeling quite inebriated and slightly boss-eyed.