Not trying to excuse the Windows app's memory usage, but these are vastly different apps. Your app is nice, don't get me wrong, but it doesn't have anywhere near the same number of features as the default weather app. In some ways that's a pro for the Windows weather app (animated radar, easy to pan around in the radar view, extra map modes, lots of graphical elements to the presentation), in some ways yours is better (ad-free, for example).

Don't get me wrong, I imagine one could get close to the same featureset while using <600+ MB of RAM, but an app that just shows a table of numbers and a static PNG for a radar isn't really the same.

FWIW, while your compiled binary is 233kB, when its running its using 2.5-4.5MB.