It doesn't actually have to rain . You could have had rain in Omaha or Denver or anywhere the plane traveled thought and if that held up the flight, then it was "weather related".
I get this song and dance every time I fly into EWR. It is either that or ATC flow control. Unless you are on the plane and it literally breaks down, you have little recourse in proving that your flight wasn't affected by the infamous "weather"or "ATC".

Without a doubt, it is one of CO's greatest shortcomings.