The problem is that the URL of the weatherstation (where the weather-app gets its info from) has changed. There is nothing that the Ubuntu-MATE devs can do about that. There has been a whole discussion about it that you can find here
The other problem is that this URL is hardcoded in the weather-app (actually, in its library libmateweather.so) and not in a config file.
That means that you either need an updated libmateweather.so file
or patch it manually.
Another problem is that 18.04 and 20.04 are no longer supported so there will not be an update of libmateweather.so for neither 18.04 nor 20.04
That leaves manually patching the libmateweather.so as only option.
Manually patching the libmateweather.so is discussed in the earlier mentioned link. You could try that if you feel you're up to it.
If you don't feel comfortable to manually patch that file then the only solution is to disable/uninstall the mate weather app and find a different app to replace it (which I think, reading from another thread, you already did )