I am having the same problem as you Bob. I am using the same version of the gweather-applet.
A simple, if inelegant, workaround until the problem is fixed by the developers/maintainers is to execute "killall gnome-panel" in a terminal after the wireless network connection is made.
I also have the same problem with the clock weather applet. I check the box in preferences to "show weather" and "show temperature" but it never shows.