I don't use the Weather Live application. It should offer in its preferences, or directly on the application a place to specify your zip code, or city/town. If it provides neither, and depends on a wireless connection, and System Preferences : Security & Privacy : Location Services : Weather Live allowed to determine your location checked, then I would look at these possibilities.
If none of the above, drag it to the Trash.
Any reason why you do not bookmark the Weather Channel page for your location, add it to your Favorites, and have that shown on your Favorites bar. Weather for your location would be one-click away. I created a Weather bookmarks folder because I have multiple link sources of weather. This folder appears on my Favorites bar, where I can select among multiple choices from forecast to color radar.
I also have Storm by Weather Underground installed on my iPhone. It can even alert you when lightning is a specified distance away.