Green’s Dictionary of Slang

1. in phr. billiard balls and stick, the testicles (and penis).

1660

Ladies Champion 4: Off goes thy stones as sure as a gun or a club to make Billjard balls on, and thy yard their Billjard-stick to play at their portalls.

2. the head (presumably of a bald person).

1882

Nat. Police Gaz. (NY) 29 Apr. 3/1: A young lady who was taken from a New York bagnio by a rich New York merchant who has a billiard ball caput [...] had a place as an actress purchased for her .

3. a hard-boiled egg.

1928

Bath Chron. 4 Aug. 25/6: The proprietor of a small city restaurant rattled off [...] ‘Two doorsteps and a couple of billiard balls,’ thick bread and butter and two hard-boiled eggs.