Nycticorax There are no weather services with open APIs. Yahoo Weather used to have one, but it has since started requiring the use of OAUTH, registering,etc. Weather Underground used to, but it has since folded into IBM services and is no longer freely available. Open Weather API requires the use of a private key, which can be set up by the user (so not ideal), and is rate limited. The same goes for Dark Sky, though they're more competitive.
Unless I was to reach out during Budgie 11 development and see if Dark Sky would be willing to "sponsor" it and have something like "Weather data provided by Dark Sky" underneath the Weather widget as some sort of "ad" (really you could think of it as a disclaimer, I've seen the same when Yahoo Weather was used by Android apps, as an example), the chances are we would have to foot the bill for a key, and that key would be specific to Solus and you'd have to provide your own during compile-time in order to gain the functionality. If I saw someone else using our key, I'd invalidate ours, push out a new package with a new key, etc.