Green’s Dictionary of Slang

1. (also tied) married.

c.1621		Beaumont & Fletcher Wild-Goose Chase IV i: I heartily desire this courtesy... This day, to see you tied, then no more trouble you.
1860		Hotten Dict. of Modern Sl. etc. 236: tied up also married, in allusion to the hymeneal knot, unless a jocose allusion be intended to the halter (altar).
1867		R. Whiteing Mr Sprouts, His Opinions 18: We wos tide up that very day three weeks.
1873		Sl. Dict.
1921		R. Lardner ‘A Frame-Up’ in Coll. Short Stories (1941) 426: And suppose you get tied up to some Boston countess and then went to New York.
1925		S. Lewis Arrowsmith 87: I was afraid the old kid was going to get tied up to – to parties that would turn him into a hand-shaker.
1936		J. Curtis Gilt Kid 133–4: Thought he was going to marry her, huh? Fancy him getting tied up with any judy.
1945		A. Kober Parm Me 32: Any young guy like you or I is a fool to get hisself tied up.
1959		D. Niland Big Smoke 150: Hell, fancy bein’ tied up to that old crab for — what — six years?
1972		B. Rodgers Queens’ Vernacular 107: gayly married. [...] tied up (mainly prison sl).
1981		G.V. Higgins Rat on Fire (1982) 57: She wasn’t very smart, or she never would’ve gotten herself tied up with Roosevelt.

2. (orig. boxing jargon) finished, completed.

1839		H. Brandon Dict. of the Flash or Cant Lang. 167/1: Tied up prigging – given over thieving.
1859		Hotten Dict. of Modern Sl. etc. 108: tied up given over, finished.
1864, 1867, 1870		Hotten Sl. Dict.
1890–1904		Farmer & Henley Sl. and Its Analogues.
1916		J. Lait ‘Charlie the Wolf’ in Beef, Iron and Wine (1917) 70: A hit would bring him in, and the game’d be tied up.
1951		D. Stivens Jimmy Brockett 12: I was getting ahead of myself. I hadn’t got Ziegler tied up, but I would have after that lunch I was planning to give him. It was as good as in the bag.

3. constipated.

1984

Partridge DSUE (8th edn) 1232/1: from ca. 1870.

4. busy, involved with.

1902		Ade Forty Modern Fables 9: I think you are tied up with a couple of Frosty Ones.
1911		G. Bronson-Howard Enemy to Society 295: I ’ain’t gunna have her think Stevey’s tied up with a bunch of lobby-gows.
1925		R. Lardner ‘Mr. and Mrs. Fix-It’ in Coll. Short Stories (1941) 412: I told him I was goin’ to be tied up and I managed to get him onto some other subject.
1929		D. Parker ‘The Last Tea’ in Penguin Dorothy Parker (1982) 185: I’m all tied up, down at the office and everything.
1936		D. Parker ‘From the Diary of a New York Lady’ in Parker (1943) 137: He was tied up.
1943		G. Marx letter 7 Apr. in Groucho Letters (1967) 152: I have been tied up since mid-January on a musical with Ogden Nash and Kurt Weill.
1951		M. Spillane Long Wait (1954) 37: Logan, you tied up right now? [...] I want to speak to you.
1956		K. Amis letter 24 Sept. in Leader (2000) 480: I have been a bit of an old fool, getting tied up with a young woman here, not to say really tied up, just started fucking her what.
1974		V.E. Smith Jones Men 181: I’m tied up right now.
1982		P. Theroux London Embassy 116: I invited him for a drink. He replied saying that he was tied up.
1999		Eve. Standard mag. 4 June 45: I’m fairly tied up in the kitchen now.
2000		G. Pelecanos Shame the Devil 38: Joe A.’s tied up, too.