In order to uninstall The Weather Channel Desktop application, you can use its uninstaller from the installation folder or Add or Remove Programs feature:
If you use Windows XP or bellow you can go to Start > Control Panel > Add or Remove Programs. In the Currently installed programs box, click on The Weather Channel Desktop program and then click Remove.
If you have Windows Vista or above you need to go to Start > Control Panel > Programs > Programs and Features. Select The Weather Channel Desktop application and click on Uninstall.