Green’s Dictionary of Slang

geezer n.2

[Lincolnshire dial. geezer, a state of drunkenness]

1. (US) a large glass of beer, slightly less than a pint.

[US]Sun (NY) 21 Apr. 7/2: If the hoister is on intimate terms with these schooners [of beer] he familiarly calls them ‘tubs’ or ‘high hats’. Some prefer to call them ‘geesers’.

2. (US) a drink of whisky or strong alcohol.

[US]Times (Shreveport, LA) 12 May 3/5: A ‘geezer o’ skat’ is a drink of whisky.
[US]Jackson & Hellyer Vocab. Criminal Sl.
[US]G. Milburn ‘Convicts’ Jargon’ in AS VI:6 438: geezer, n. A drink of any high-powered booze.
[US]A.J. Pollock Und. Speaks.
[US]Goldin et al. DAUL 77/2: Geezer. [...] 2. A drink of potent liquor.