I tried gnome-weather on two of the other UM 24.04 LTS computers and I could reproduce the same issue as you described 
Read on:
After installation of gnome-weather and setting the location, the link with "Weather data from Norwegian Meteorological Institute" seems to be missing.
BUT: it turns out that it's not missing, it is there but just invisible.
WHY?:
GNOME introduced their own theming setup which is completely incompatible with everybody else. This is not the first time that the community must deal with the fallout of "the GNOME way" of doing things.
After installing, the theme of gnome-weather does not get initialized because MATE does not themes in "the GNOME way" so some colors (like the links) are blank.
HOW TO SOLVE?:
I forced gnome apps to follow my theme by adding this line to ~/.profile:
export GTK_THEME=Ambiant-MATE-Dark-Red:dark
And then the colors got initialized and the problem solved.
You probably want something else depending on your theme and I saw you prefer light, so the syntax is:
export: GTK_THEME=your_MATE_theme:light
So if you have default Yaru the line should be:
export GTK_THEME=Yaru:light
log out and login again and start gnome-weather.
You'll see that the link has appeared.
Oh, and don't forget to file a bug here: