If spybot removed the backweb program, it won't show up again, but any program that depends on it to run will complain that it's gone. AFter a shut down restart, see if you still get the message. If you do get it, search for the program or process it mentions in the warning message, and try to uninstall or delete it.
There are a couple of things that I would suggest you try, the first being to install and run AdAware SE. It catches things that Spybot doesn't, and vice-versa. Having at least two different malware detectors is a good idea. If you find another that you like, add it on.
Also, check what processes are running in the background. To see the list, press ctrl-alt-del and click on the Processes tab in the window that comes up. This is a list of most of the things going on in the background, which is where you can identify a lot of malware programs. Check
www.processlibrary.com and
www.blackviper.com for more info on processes and how to work with them. Getting an idea of what is versus what should be running on your machine will help you to understand and repair the problems. Blackviper has a couple of good guides for tweaking this stuff, and some generally good advice.