Usually a corrupt cache. The following procedure will resolve most xxxx app has stopped error messages.
If you are using a weather widget on your homescreen, drag it to the trashcan. Then go into the settings menu > applications > all > application manager > weather and click force stop, then clear cache, then clear data.
Then boot to recovery mode (pull battery, replace it, then press and hold in order the volume up key, then the home key, then the power key). Once the screen turns on, release the keys and from recovery mode, wipe the partition cache (or wipe cache + Dalvik if you have a custom recovery).
That should clear up corrupt or messed up weather settings. You will have to drag your weather widget to your homescreen again to replace it.