@jkolsing: I am not sure what Opera means by "Browsing activity". It is probably means that extension tracking when you click on link " ← Set this as place for extension", and remember selected place in browser storage. Extension using this place to download related weather forecast.
If you worrying about tracking. Then you can check source code of this extension, it is open source, and as you can see it do only weather related stuff
https://github.com/vo-va/tiny-weather-forecast/blob/master/background.js