I sent a message to Accuweather and this is what they sent me. It worked for me, and I hope it helps.
Thank you for using the AccuWeather.com Web Signals service.
We are sorry you are experiencing this issue. Please access the following URL in your BlackBerry mobile web browser. http://push.na.mobile.blackberry.com/mss/PM_subList
This will list all of your Web Signals subscriptions. Check the box next to the weather Web Signals and hit the unsubscribe button at the bottom of the page. You can then re-subscribe for the service by going to http://www.accuweather.com/blackberry/push/signup.asp
AccuWeather, Inc. AccuWeather.com - Wireless http://www.accuweather.com