MiTeC Weather Agent is a free app that enables you to view your local 5-day forecast, and it also includes moon phases as well as sunrise/sunset times for your region.
The locale is selectable so some specific towns, etc., may not be included. There is some mild customization available like the color scheme for instance. And you can readily change between metric and imperial temperature displays for C or F.
MiTeC Weather Agent does allow you to select desktop placement and display type between full (5-day) or partial (current) display, but it is not able to be minimized, unfortunately. That said, it does give quite a bit of information relating to your selected area including humidity %, wind speed/direction, cloud coverage, air pressure, and precipitation totals.