You mentioned in your earlier post that you'd restarted the phone already with no change. You also deleted and replaced the widget with no change. Did you try removing the battery for a few minutes? The weather widget needs a good data signal to update. Is there any problem with the service in your area? If you have WiFi available, does it make any difference if you're connected to WiFi? Has your phone received the (OTA) software update? If not, then I'd try installing it manually by going to Settings->About Phone->Software Update, then choosing to check now. If you've already received and/or installed it, then you might try a factory reset.
I know you said you really liked the weather/clock widget, but a lot of owners get rid of the native widgets early on and use an alternate (home screen) launcher that they're familiar with and have used on other phones. Often these alternative apps are more reliable and have smaller resource demands too. I know animated widgets are fun and attractive, but widgets by design constantly use system resources (processor and RAM). If you have many screens loaded with widgets, you may be robbing your phone of considerable power. For example, I used to run seven screens with a great many widgets and available RAM hovered around 100mb. I reduced the number of screens to three and eliminated nearly all the widgets I'd been using (substituting shortcuts to open the apps instead, as they use no RAM) and I now have consistently 145mb of available RAM. My phone is much snappier and performs more reliably than before. I use GO Launcher EX and none of the native widgets. I use a simple weather app and clock that takes a fraction of the power of the native app. There are many things you can do to improve the way the phone operates.