Think of it as handing something a standing it did not have. The thing already exists; what it lacks is the right to be treated as proper. Then one act — a law, a signature, a marriage, or simply being shown often enough to look ordinary — gives it that right.
legitimize 可以想成「給一樣東西一個名分」。那樣東西本來就已經存在了。它缺的不是存在，是被承認。然後有一個動作把名分交給它。可能是一條法律、一個簽名、一場婚禮。也可能只是不斷被當成很平常地呈現出來。做完這個動作，它就有資格被當成「正當的」來看待。三種用法的差別，只在名分是誰給的，以及給得正不正當。
From the word’s history
The word is legitimate + -ize, where -ize means 'make into'. So it is literally 'make legitimate', which is exactly what every use does.
這個字由 legitimate 加上字尾 -ize 組成，-ize 的意思是「使成為…」。所以字面上就是「使某件事成為 legitimate」，跟三種用法的共同點完全吻合。
Wiktionary entry for legitimize, etymology_text supplied in this packet ('From legitimate + -ize'; source_ref kaikki:3f6f69a190036ae4:1071117861:11944)
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