It seems weather is working again, after the last update (the one that changed the name of the app to MS Band). At least, I'm getting updates. Haven't got weather updates ever since update to windows 10 anniversary update.
I had still been getting updates, but it almost always showed the last update was performed the night before. I noticed Saturday that the weather tile had started updating regularly throughout the day with the latest updates, but I'm not sure if it was the Windows 10 build or the Health app and Band firmware that did the trick.