Here is the Asus Weather widget and works great and no rooting needed, just download on your computer and then email the apk to your self on the tablet, open and install and then reboot your tablet and that's it. In setting you must allow unknown source for downloads first.
Scroll down and select the Weather_signed.apk
Working My Water live wallpaper & more from Asus Transformer! - xda-developers
Scroll down and select the Weather_signed.apk
Working My Water live wallpaper & more from Asus Transformer! - xda-developers