There's some sort of problem updating either the first location, or the current location. Can't tell which since they're the same for this home-bound iPad. Opened the app just now and the last update was 3 hours old. Swipe to another location, updates promptly. Back to first location, still old info. Go to Home screen, swipe right to view widget, updates fine. Then the app also has current data. It seems as if opening the app does not immediately trigger an update, nor does any subsequent action. But the widget is implemented to work as you'd expect.
Edit: If I leave the app running, it updates promptly when opened. The problem occurs if I force-quit the app. Then when I open it the first location remains frozen at the previous time it was viewed. Apparently, starting the app does not trigger an update. I choose to force-quit BeWeather because it holds as much as 13,000 pages (16 KB) of processor memory (not storage), which is inconvenient for my other apps. That's 200 MB of useful space.