Personally, I would be very hesitant to make a universal interpretation of a symbol (the spider) that isn't interpreted in the Bible. IMO, if it's not in the Bible, it can really go in quite a few directions depending on the culture and on how God is using that particular symbol.
A brief search of the Bible reveals (depending on your translation) 2-3 references to spiders in all of scripture. 1-2 of them are about the spider's web, and use it as an allegory for weakness.
Job 8:14 (NIV)
What he trusts in is fragile ; what he relies on is a
spider's web.
Job 27:18 (ESV)
"He has built his house like the
spider's web,Or as a hut which the watchman has made.
An uncommonly translated verse has:
Proverbs 30:28 (NKJV)
The
spider skillfully grasps with its hands, And it is in kings’ palaces.
The other main reference is:
Isaiah 59:5 (ESV)
They hatch adders' eggs and weave the
spider's web;He who eats of their eggs dies,And from that which is crushed a snake breaks forth.
Two primary refs are Job 8:14 and Is 59:5 though, and neither one give a clear definition of what a spider is symbolic of. Therefore I would put little weight in saying that a spider symbolizes either witchcraft, demons or sin, unless the dream itself suggests that as an interpretation. In that case, it still wouldn't be evidence that a spider is symbolic elsewhere of witchcraft, demons or sin, because it's not scriptural.
Anyway, I'm really interested in what spiders might symbolize, because I've had several perplexing dreams that involve spiders. Here's a segment of one of those dreams:
[I'm in a bright, sunny park and] God was there physically in human form, explaining things to me. I don't remember what He looked like. Suddenly a spider starts dropping down from the sky, and God says that the spider is a real prophetic symbol. Then we leave and I'm in my home, and many spiders and other animals around, and God starts talking about waiting and observing to see if a creature is hostile or not. Essentially what He says is that you can't assume any given animal is hostile, you have to wait to see if it is or not. Some of the spiders hiss and jump at me, and I command them to die, which they do. So I have power over them.... [continues in another theme]
So I can understand if you want to say that "spiders and many other animals" are symbolic of demons at that point, but what about the first spider dropping down from the sky? Why would it appear in such an otherwise bright, clear scene?
In my other dream, here's what I wrote:
"Had a dream that spiders only recently came to mean demons, and that they used to have neutral/good connotation. (check Bible)"
So perhaps you can see why I think we should be careful about how to interpret spiders. And yes, that's verbatim what I wrote when I woke up from the dream, and no, I have absolutely no recollection of what the dream was, other than that it involved spiders that weren't evil.