OK, actually, it just did it now, saying "Unable to fetch current conditions." But, I have to minimize the app and open it again to make it refresh. A button would've been nice (it refreshed then fine when I opened it again; weird fluke I guess).
I have the same issue; when I open the full app, I have to click refresh manually,or the data is that from the last time I refreshed, potentially days or weeks old. The widget refreshes appropriately.
Android 5.1.1, Cyanogenmod 12.1, OnePlus One