BAckweb is usually packaged with software. It is just an annoying process that updates the software periodically.
http://www.securemost.com/articles/trou_3_remove_backweb_client.htm
Your spyware has cleaned the DLL out of the system but left the startup file in your boot seqence. If it is not listed in you Add/Remove programs applet, you can uninstall the files manually or simply stop it from loading/trying to load at boot.
I am not sure what operating system you use but here's a couple of ways to clean it up.
1) Win95/98 Click [b]START>RUN[/b]and type [b]MSCONFIG[/b] in the [b]RUN[/b] dialog box.
Select the Startup tab and scan down for the entry that loads backweb.dll, uncheck the box beside it and reboot.
2) For Win200 or XP, you can download the XP MSconfig file from here and it worhs the same for Win2K.
http://www.perfectdrivers.com/howto/msconfig.html
The first link also provide complete manual file removal instructions if you are comfortable weeding through your registry. Just don't forget to export a backup copy of the registry first.