Have you checked where Garmin gets the weather data from for your location?

Bernd said:

By the way the airport Garmin thinks is "my airport" is located more than 120km away from my hometown

Is this the closest weather station/airport to your location and is it the fixed weather data for all your activities regardless of where you do them?  120km/74.5 miles is quite excessive.   I just took a look at my previous activities and when doing activities "at home", my weather data came from a small single engine airfield 1.5 miles from my house even though I'm 10 miles from a major airport.  When doing activities outside of my home area (hiking in the Cascade mountain range for example) I received data from a Ranger station rather than an airport/airfield.  My weather data has always been pretty accurate.

Bernd said:

Garmin has no influence on this.

Bernd said:

the airport Garmin gets the weather data from.

Garmin isn't getting the weather data.  It's requesting weather data from your phone.  I think it depends on your phone/carrier on where it's getting the data.

Not always a combination of four letters....

i am from Slovenia and i have code 14219 and i cant find any information on this.

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.

Bernd said:

If the next airport is crazy far away or there are mountains I guess for safety reasons they fill some gaps with additional stations.

I see what Chris wrote about regional airports, but this obviously isn't the only source of data as my ranger station data shows and I was still within 120km from an airport.  It must request the weather data from a specific source type that's normally found at airports, but not airports exclusively.  Am I to assume correctly that you're phone weather app which uses cell towers for your location differs from your watch weather?  I'm interested to know if the 5 numeric codes others have is for airports or other sources.

Bernd said:

The fact that Garmin uses this data for gadgets like sports trackers is a total joke in my opinion.

Another problem you'll face if your data is coming from weather station is 120km away is your FirstBeat  'heat and altitude acclimatization" data if there's a significate difference between the two.  This is something Garmin should look into changing for people in your situation.

The phone is only used for internet connection. Otherwise the connect app couldn't pull the data from the internet. It has nothing to do with the phone carrier or some weather app on the phone. 

Yeah I checked some activities in my history and sometimes I also find the 5 digit code. Those are WMO numbers. Here is a list which is probably not complete but maybe you find yours. 

http://weather.rap.ucar.edu/surface/stations.txt 

I just wished the locations would not be so encrypted. 

Looks like a WBAN (Weather Bureau Army Navy) identifier. It's located in Croatia close to Slovenia. 

Does this location make sense to you?