The Legalist philosopher Han Fei read 公 as a moral equation: 八 'to divide, turn away from' over 厶 'private' — to turn your back on the private is to be public-minded. Whether or not that's the true origin, China taught it for two millennia.
公 stamps everything shared: 公共汽车 public bus, 公司 company, 公园 public park, 公斤 kilogram. It's also 'fair' (公平) and a respectful 'grandpa' (老公公) — and 老公 is slang for husband.
Divide 八 away what's private 厶 — what's left is PUBLIC and FAIR.
公 is the 'kilo-' in Chinese metric: 公斤 kilogram, 公里 kilometer — 'public catty' and 'public mile', the fair standardized versions of old market units.