Green’s Dictionary of Slang

heavy man n.

also heavy guy, heavy worker
[heavy n. (3b)/heavy n. (4b)]

1. [1910s+] a safebreaker.

2. [1920s] (US Und., also heavy gun) a gang leader, a senior racketeer.

3. [1930s+] a thug, a criminal who is prone to use violence.

4. [1990s+] (W.I.) an influential man.