已 is a curled stroke closing on itself — likely a variant of the snake-like 巳 from the zodiac branches. The loop closing = the matter closed: already done. Compare 己 (self, fully open) and 巳 (fully closed): 已 stops halfway, a door swinging shut.
已经 (already) is 已's day job: 我已经吃了 ('I already ate' — the polite dodge of every second dinner invitation). Formal writing uses bare 已: 已完成 (completed), stamped on forms and delivery updates across China. The 己/已/巳 trio — open, half-closed, closed — is the classic handwriting trap that Chinese schoolchildren drill for years: three near-identical curls, three different words.
The curl half-closed — the matter is closing: ALREADY.
己已巳 — open gap = self, half gap = already, no gap = zodiac snake. Three curls that terrorize handwriting class.