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.
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)
From the picture
讓不對的事看起來站得住腳
同樣是把名分交出去，只是這次交的人沒有那個權力，而拿到名分的是本來不該被接受的事。法律上什麼都沒變，變的是大家怎麼看。
verb · C1
To make something that is unfair or morally wrong appear acceptable and normal, usually by treating it as ordinary, showing it often, or giving it public support.
使…顯得正當、合理化
verb · C1
To make something official, legal, or accepted as proper, especially when a government, a court or another body with authority gives it formal approval.
使合法；使正式取得地位
verb · C1
When parents legitimize a child, they marry each other so that in law the child then counts as the child of a married couple.
使（子女）取得婚生身分