A hand with a tool making a change — gēng, to alter, to renew. Each change advances a degree, so gèng became the comparative booster: even more, still more.
更好 even better, 更多 even more — the upgrade word. As gēng: 更新 update (your apps live on it). Ancient nights had five 更 watches; 三更半夜 'third-watch midnight' still means the dead of night.
Strike a CHANGE (gēng) — each change takes you a step FURTHER (gèng).
半夜三更 'the third night-watch' survives from when Chinese cities marked time by drum towers — roughly 11pm to 1am.