At least according to the wiki entry for the Morai (Emphasis mine):
In Shakespeare's Macbeth the Weird sisters (or Three Witches), are prophetesses, who are deeply entrenched in both worlds of reality and supernatural. Their creation was influenced by British folklore, witchcraft, and the legends of the Norns and the Moirai. Hecate, the chthonic Greek goddess associated with magic, witchcraft, necromancy, and three-way crossroads, appears as the master of the "Three witches". In Ancient Greek religion, Hecate as goddess of childbirth is identified with Artemis, who was the leader (ηγεμόνη: hegemone ) of the nymphs.
Along with the Greek/Norse, there are the Weiße Frauen, or White Ladies, which are echoed by the Witte Wieven (Dutch) and Dames Blanches (French). All of these are literally "white ladies" (quite often depicted in threes) who have supernatural influences. (Jacob Grimm later attempted to codify the Weissen Frauen as Holda, Perchta and Ostara/Eostre. Eostre is the namesake of the festival of Easter).
TL; DR - It looks like the origins are a cobbling together by Shakespeare of several similar legends of influential women trios.