Quote from WeatherBug Support:
http://weather.weatherbug.com/support/weatherbug-mac.html#cantDelete
+# WeatherBug Lite doesn't run, but I can't trash it either. The finder keeps telling me "Cannot delete because program it is still open." How do I get rid of it?+
"For some reason, WeatherBug is still running on your system without displaying an interface. If you are the administrator of the computer, or have administrator access, you can quit the WeatherBug Lite application by opening up the "Terminal" and typing killall "WeatherBug Lite". If you do not have administrator access, follow the instructions for uninstall here. Be sure to move WeatherBug Lite to the trash (even though you can not delete it) and restart your machine. After restarting you should be able to empty the trash -- removing WeatherBug Lite from your system."