There are spider legends and stories in many, many mythologies,
Celebuial, so I don't think anyone can say that other authors copied Tolkien. If you do a google search for spiders in mythology, you will find many links, but here are some of the best known stories.
Anansi, the trickster god in African legend
Some Japanese spider myths
The story of Arachne in Ovid (Greek)
Some North American spider/weaving stories of creation
Not all of these mythic stories involve evil
per se, but the link between weaving and creation is clear. Tolkien seems to have suggested that the spider goddess created an early form of the world before Eru and he decided to represent this as evil and disgusting. And the Downs is often overrun with 'search spiders' of course!
Have fun googling on the modern web!