If your favourite weather app suddenly stopped working in the last week or so, there's no point trying to refresh or reinstall it. Google has shut down its weather API without a word and stranded developers who relied on it to power their weather-related applications. What we're left with is a pile of broken apps that may or may not get fixed.
It turns out that developers using Google's weather API were doing so without authorisation. The private API was only intended to serve weather data to the now deprecated iGoogle service, but its simplicity made it popular with third-party developers. So while it's perfectly understandable for Google to close the API along with iGoogle -- and it has every right to do whatever it wants with its own API -- the lack of communication has left everyone scratching their heads.
There are a few things you can do to try to fix the problem. Some apps offer alternative weather services such as Yahoo or World Weather Online -- so have a dig through the app's settings to see if you can switch the source from Google Weather to something else. If that's not an option, check the app's page on Google Play or iTunes or wherever, and then the developer's website. Warning messages have been added to the descriptions of affected apps in some cases, which means it's simply a matter of waiting for the developer to push out an update.
If your app is affected but so far unacknowledged, email the developer and ask what's going on. I know of at least one developer who has made his app unsearchable on Google Play while he tries to fix his app, and another website has shut down altogether. So be prepared to ditch the app and hope that the next one doesn't have the same problem. Unfortunately, there's not a lot we can do about developers using unsupported APIs and Google pretending that nothing happened. We'll just have to keep holding the mess they made.