Green’s Dictionary of Slang

to drink, esp. in small sips.

1769		Trinculo’s Trip 25: I was tiffing a stout cann of flip [OED].
1785		Grose Classical Dict. of the Vulgar Tongue.
1812		W. Combe Doctor Syntax, Picturesque (1868) 15/1: He tiff’d his punch, and went to rest.
1821		W. Combe Doctor Syntax, Wife (1868) 339/2: There he tiff’d his punch and talk’d and smok’d.
1844		J.W. Kaye Peregrine Pultuney I 227: For people do tiff at the Cape of Good Hope. as every body knows.