Green’s Dictionary of Slang

1. a safebreaker.

1914		Wash. Post 11 Nov. Miscellany 3/5: The boxman has a string of monachers such as ‘peterman,’ ‘yeggman,’ ‘blaster,’ ‘heavyman’ and ‘soup man.’.
1920		C.S. Montanye ‘Perfect Crime’ in Penzler Pulp Fiction (2007) 355: Young, ambitious crust-floppers, grifters and heavymen.
1926		J. Black You Can’t Win (2000) 237: It was the kind of safe that discourages the ‘heavy man’ (safe breaker).
1928		M.C. Sharpe Chicago May (1929) 260: Heavy Guys — stick-up men, or safe-breakers.
1930		Miami Herald 31 Aug. 22/1: When the toughest ‘heavy-worker’ in the land came to he was locked in the hoosegow.
1935		A.J. Pollock Und. Speaks n.p.: Heavy worker, a safe-blower.
1937		‘Boxcar Bertha’ Sister of the Road (1975) 72: Two of the ‘heavy men’ (burglars) I met that night were killed by policemen soon after.
1949		Monteleone Criminal Sl. (rev. edn).
1950		Goldin et al. DAUL 93/1: Heavyman. [...] 2. A safe-cracker, especially a specialist in ripping.

2. (US Und., also heavy gun) a gang leader, a senior racketeer.

1929		Hostetter & Beesley It’s a Racket! 227: heavy guy — Head of a ‘mob’ or racket.
1935		A.J. Pollock Und. Speaks n.p.: Heavy guy, a boss.
1949		Monteleone Criminal Sl. (rev. edn) 115: heavy gun [...] heavy guy A gang leader.

3. a thug, a criminal who is prone to use violence.

1931–4		D. Clemmer Prison Community (1940) 332/2: heavy man, n. [...] 3. A bruiser or killer for a mob.
1940		D. Maurer Big Con 167: John Singer, an old heavy-man.
1950		Goldin et al. DAUL 93/1: Heavyman. 1. (Scattered; chiefly Pacific Coast) An armed robber.
1962		Ragen & Finston World’s Toughest Prison 803: heavy man – An armed watcher in a gambling house.
1995		Francis-Jackson Official Dancehall Dict. 24: (H)eavy-man [...] 2. an armed man.

4. (W.I.) an influential man.

1995

Francis-Jackson Official Dancehall Dict. 24: (H)eavy-man 1. a man of influence; influential person.