Green’s Dictionary of Slang

sore-eyed, squinting; thus wapper eye n., a sore eye, a squint.

1604		Middleton Black Book line 457: [I] therefore changed my shape into a little wapper-eyed constable, to wink and blink at small faults.
1608		R. Armin Nest of Ninnies 6: Such was his, who thus busied, was took napping by the weale publike, who smiles upon him with a wapper eye.
c.1698		B.E. Dict. Canting Crew n.p.: Wapper-eyed, that has Sore or running Eye.
1725		New Canting Dict. [as cit. c.1698].
1737, 1759, 1760, 1776		Bailey Universal Etym. Eng. Dict. [as cit. c.1698].
1785, 1788, 1796		Grose Classical Dict. of the Vulgar Tongue.
1811		Lex. Balatronicum.
1823		‘Jon Bee’ Dict. of the Turf, the Ring, the Chase, etc. 190: Wapper-eyed — heavy-eyed, drunk, so that the eyelids lose the retractile function, occasionally.
1838		W. Holloway Dict. of Provincialisms 184/1: Wappereyed, Goggle-eyed [...] or squinting.