Green’s Dictionary of Slang

1. to gradually diminish the quantity or potency of one’s drink.

c.1930		(ref. to late 19C) N. Kimball Amer. Madam (1981) 251: They felt, Frank said to me, if he tapered off in a whorehouse, he wouldn’t drink so much at home or try and screw any lady guests of his sisters staying with them.
1940		E. O’Neill Iceman Cometh Act II: I can’t spend my life sitting here with you, ruining my stomach with rotgut. I’m tapering off.
1968		J. O’Grady Gone Troppo (1969) 10: The best way to start taperin’ orf is to put some coffee in your rum.

2. (drugs, also taper down) to withdraw from narcotics by gradual reduction of dosage.

1910		Wash. Post 3 July 3/1: Listen ter the dope [...] Why, he couldn’t even taper down, let alone break off.
1915		Atlanta Constitution 1/4: The loot seized at the time of the arrests comprised [...] a box of Chinese medicine for tapering off from the opium habit.
1933		‘Paul Cain’ Fast One (1936) 206: Maybe I’d better have one more load in the arm, Doc -to sort of taper off on.
1948		W. Burroughs letter 30 Nov. in Harris (1993) 25: I hope to rid myself of the habit in the course of this trip. Taking along a pint of P.G. and a large supply of goof balls to taper off.

3. (drugs, also taper) to force someone to withdraw from narcotics by reducing their dose.

1952

(con. 1948) G. Mandel Flee the Angry Strangers 477: They’ll taper him ... They’ll sit him oud on Riker’s Islan’.