Green’s Dictionary of Slang

1. (US) alcohol; a drunken spree.

1834		W.A. Caruthers Kentuckian in N.Y. I 23: Stranger, won’t you join us in a glass of tight?
1855		‘When I Went Off to Prospect’ in Lingenfelter et al. Songs of the Amer. West (1968) 110: At Deadwood I got on a tight.
1880		Bulletin (Sydney) 20 Nov. 12/1: Some [actors] put tights on, whilst others ‘get on tights’.

2. a drunkard.

1926

Maines & Grant Wise-crack Dict. 12/2: Pair of tights: Two drunks.