You can configure your ZIP and other behavior in the "Config" section to the lower left. There you can also select "Center on ZIP".
You can also click on "update" to store the location of the map.
The configuration of US Weather Radar can be stored in the Google(tm) cloud with the "Save with Google(tm)" button in the config menu. This saves the configuration data (about 1kbyte data) in a hidden application folder in Google drive. The application has no access to other data than its own application folder.
If you have issues with your configuration disappearing when you close the browser you can opt-out for config deletion for certain web pages in the Chrome configuration. The option to save the data in the cloud might be very helpful as well.
If you still have issues with saving your configuration please make sure extensions blocking Google APIs and other functions (Disconnect, ...) are disabled by "whitelisting" US Weather Radar.