Actual spiders are great, if you have them, since they'll eat pest insects. Don't worry about that.
But by the description, I'm actually a bit concerned about spider mites.
Spider mites are frequently red, and they can make "web" like material (that's why they are called SPIDER mites).
But they shouldn't be as large as BBs (which are roughly 4.3mm in diameter, or 0.172 inches), and they shouldn't spin actual "spider" webs.
If you have spider mites, they'll typically live on the UNDERSIDE of your leaves, and you can see them more easily with a hand lens or loupe. They'll also suck the juices out of your leaves, leaving lots of little white or yellow spots on the leaves. If you can see either of these things, you've got to deal with the mites asap, because the infestation can severely injure your plant, spread to other plants, and even durably contaminate your grow area, infecting future grows.