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Spyware is software installed on the back of other software (like Kazaa), and usually transmits information about what you do back to it's HQ, which sells the data on to interested parties. Were you to uninstall Kazaa, the spyware would stay on your machine.
To remove it, visit http://www.lavasoftusa.com/aaw.html and download adaware. It's a damn fine tool for eradicating spyware from your machine. Be warned - Kazaa might not start afterwards, complaining that "vital files" are missing, but as you say Kazaa Lite does the job just as well :O)