You need to check out an activity on the Garmin Connect webside (mobile doesn't give away the source).
Expand the weather icon on the top right of the map. There you find the ICAO code of the airport Garmin gets the weather data from. It is always a combination of four letters. Google the code or put it in here:
https://www.icao.int/safety/iStars/Pages/Weather-Conditions.aspx
These airports are the only source and how frequent the weather widget updates depends on the airports and some fancy algorithm. Garmin has no influence on this.
Point is the weather data is only useful for pilots and other aviation purposes. The fact that Garmin uses this data for gadgets like sports trackers is a total joke in my opinion.
By the way the airport Garmin thinks is "my airport" is located more than 120km away from my hometown. I wonder how reliable that weather data is
How far off is your location? Maybe we can have a little competition


This was posted by Garmin Chris in the sticky post about the weather widget. So even Garmin admits the data is pretty much useless unless you are lucky enough to live very close to one of these airports. If the next airport is crazy far away or there are mountains I guess for safety reasons they fill some gaps with additional stations.