I mean, even though it acts like one and it does mess up your computer (IMO), Backweb is a program, not spyware. It goes into your registry, finds certain programs it recognizes, and every so often searches the home pages of the companies that put out the software for updates, then autodownloads the updates for you in the background. Great, unless you actually USE your computer and your internet connection.
What I'm saying is you had to install it. Probably it came bundled with something else you installed and you just didnt notice it. Go to your Control Panel -> Add/Remove Programs and see if it is in the list. If it is, tell Windows to uninstall it. No more backweb.