You don't mention what device, OS, or widget you are using, so I can only answer in general terms. Weather widgets are usually configurable to find your location by GPS or network triangulation (less accurate). GPS or starting your phone in wifi will usually provide the most accurate results. If OTOH you are referring to chosen locations, rather than auto-detection, probably the easiest way to clear this up is to go into Settings > Manage apps, and then "Clear cache" and "Clear data" on the app/widget in question. After restarting your phone, reconfigure weather location and all should be well.