I think this association may also go back to the goddess Arachne, something of a sorceress, and the fates associated with magic. The idea of "weaving a web" is a metaphor used to    describe magic, as well as the idea that a spell to control others etc. can be "woven."

In any case, modern witchcraft/wicca is full of the imagery: "Then weave the web of the mystic measure, from the depths of the sky to the ends of the earth; come swift spirits of night and of pleasure, and fill our dance with the music of mirth."