OK. Figured it out. Here's how to get the BW animated screen active on unlock...
1 -- No Launcher Pro/Plus. If you want the BW animated weather screen active on unlock, at least the way things are now, you can't have LP+ ... *sob* ... Uninstall. Do battery pull (60 seconds out then reinstall battery and turn on).
2 -- Uninstall Beautiful Widgets and BW Live Wallpaper. Do another battery pull.
4 -- Re-install BW Widgets and BW Live Wallpaper. In configure, make sure the "Unlock Animations" (after unlocking the device) is checked in the Advanced section.
After installation, I did another battery pull, just to be sure. Probably wouldn't have been necessary, but I was making so many changes (including setting up the stock home screens with widgets and shortcuts), I thought it would be helpful for the X to handle it all.
It works now! The question is: What's more important - weather animation on the home screen OR Launcher Pro Plus. Tough one... or not.