妹 = 女 (woman) + 未 (wèi, 'not yet'). A lovely logic: the 'not-yet-grown' female of the family = the younger sister. The 未 also hints at the sound (wèi → mèi).
妹妹 (mèimei) is a younger sister (older = 姐姐). 姐妹 together = 'sisters'. In casual modern speech, 妹子 or 小妹妹 can address a young woman, and online 妹子 just means 'a girl'. Family-term precision again: Chinese always marks older vs younger.
The 'not-yet' (未) grown woman (女) of the family — younger SISTER.
妹 hides 未 ('not yet') inside — the not-yet-grown one. Pair 姐妹 (older+younger) and you've named all the sisters in one word.