How to delete doubled weather widget in El Capitan?
7 simple steps to solve the problem (works even in OS X 10.11.1):


Go to /private/var/db/locationd/ from your finder or terminal;
Give you full privilege to change files inside this folder;
Convert clients.plist file from binary mode into xml1 by running this command in your terminal: sudo plutil -convert xml1 /private/var/db/locationd/clients.plist;
Open the clients.plist and remove the key and dictionary pair in the configuration file. For my case I delete all fields that includes weather word;
Don’t forget to convert back the client.plist into binary file using the command below in Terminal: sudo plutil -convert binary1 /private/var/db/locationd/clients.plist
The prelast step is to restart the daemon that monitor the change of location. Type this command in Terminal: sudo killall -KILL locations;
Finally com.apple.ncplugin.weatherdisappeared from Location Services, I reaccepted to check my weather by location and everything starting to work perfectly.


This article helps me.