Indirectly, what are your rights in that case? Say KLM has many aircraft stranded at CDG due to bad weather there, and has to cancel your UK flight due to no aircraft being available.

Yes, weather is the ultimate cause..but not for your specific departure/arrival airports. Would compensation be due?

As for the OP case: in the end it does not really matter if the aircraft did or did not arrive. They said it was due to weather and that was not the case - weather was fine where you were, as was AMS. So personally I would push this a bit more and let them explain what weather event canceled the flight..?