I wonder how it can prove it's got no weapons if it hasn't got them.

Same way South Africa did when it disarmed. Compare the history of the Iraqi disarmament, with its constant deception, concealment, and non-cooperation, with the nuclear disarmament procedures in South Africa, which were marked by eager and conscientious cooperation with the U.N. South Africa was the first example of a nuclear-armed nation that voluntarily and successfully gave up its nuclear weapons programs.

I have posted links to chronologies of the U.N.'s attempts to get Iraq to comply with various agreements, many of which were conditions to the Gulf War cease fire. They show that Saddam dragged his feet the whole way. This perception that he was not at all interested in disarming, and was in fact concealing many things, went a long way toward convincing people that he was in fact a threat.

If he didn't have any arms, he sure as hell didn't act like it.