哥 is two 可 stacked up. Surprisingly, it originally meant 'to sing' — it's the ancestor of 歌 (gē, song)! It was borrowed to mean 'elder brother', and the singing meaning moved to 歌. Same sound, gē.
Chinese family words are precise about age and hierarchy — there's NO generic word for 'brother'. 哥哥 (gēge) is specifically an OLDER brother; a younger brother is 弟弟. This reflects how much birth order matters in Chinese families. 大哥 ('big brother') is also a respectful way to address an older man, or the leader of a group.
Two 可 stacked — once 'to sing', now your big BROTHER.
Chinese has no generic 'brother': you must say older (哥哥) or younger (弟弟). Same for sisters (姐姐 / 妹妹). Age and order are built right into the words.