Green’s Dictionary of Slang

drop in one’s eye n.

[? SE drop of liquor, or one is on the verge of drunken tears]

a state of (near) drunkenness.

[UK]B.E. Dict. Canting Crew n.p.: Drop in his eye almost drunk.
[UK]New Canting Dict. [as cit. c.1698].
[UK]Bailey Universal Etym. Eng. Dict. [as cit. c.1698].
[UK]Grose Classical Dict. of the Vulgar Tongue n.p.: Drop in the eye, almost drunk.
[UK]C. Dibdin Yngr Song Smith 128: But the drop I like best is a drop in my eye.
[US]M.L. Weems Drunkard’s Looking Glass (1929) 73: With a ‘drop in his eye,’ he skipped into a carpenter’s shop, and reached his hand to the whiskey bottle.
[UK] ‘Thinks I To Myself, Thinks I’ Universal Songster I 25/1: No wonder she’s blind with a drop in her eye.
[UK]‘A Drop in the Eye’ in Convivialist in Spedding & Watt (eds) Bawdy Songbooks (2011) IV 7: And what is it causes the peaceful to brawl, / And makes us see double, or else not at all? / ’Tis a drop, a drop in the eye.
[US]North-Carolinan (Fayetteville, NC) 18 Nov. 1/6: Drunk [...] primed, slewed, half-slewed, half-snapped [...] a drop in his eye.
W. Mixx Advertiser 28 July 4/3: Mr Shield [...] got a drop in his eye [and] broke some bottles and a pane of glass.
[Scot]Dundee Courier 5 Mar. 5/5: Dempster appeared at the bar with a ‘wee drop in his eye’ [...] and dismissed with an advice to leave drink alone in the fiture.
[Scot]Eve. Teleg. (Dundee) 8 Mar. 1/5: With a Drop in his Eye [...] David Jack [...] charged with having been drunk and incapable.

In phrases

have a drop in one’s eye (v.)

to be tipsy.

[UK]Swift Polite Conversation 9: O faith, Colonel, you must own you had a Drop in your Eye: when I left you, you were half Seas over.
[UK]Gent.’s Mag. 559/2: To express the condition of an Honest Fellow [...] under the Effects of good Fellowship, [...] It is also said that he has [...] 51 Got a drop in his Eye.
[US]T. Haliburton Clockmaker II 162: It was lucky for me she had a wee drop in her eye herself.
[Aus]Bell’s Life in Sydney 8 July 3/3: He considered him to have a drop in his eye.
[Ire]J.E. Walsh Ireland Sixty Years Ago (1885) 60: Though he did not weep, he certainly had a drop in his eye.
[Aus]Bell’s Life in Sydney 22 May 5: He ran foul of the old woman, who also had ‘a wee drap in her een’.
[Scot]Paisley Herald (Renfrewshire) 10 Feb. 6/3: Jodge Boyd [...] possessed a similar weakness [...] when passing sentence of death [...] he sldom failed to have a drop in his eye.
[UK]Shaw Pygmalion II: Youd had a drop in, hadnt you?