Just managed to get it working again but still don't have a clue where the problem is.
I uninstalled and reinstalled it again. I could then open the applet (the widget was still gone) and could delete all cities. I also disabled animation and already uninstalled all icon packs. Then I entered the cities again using gismeteo.ru only. It took some restarts of the desktop but for now it works again.
I guess it's related either to the stations in weather.com or to the animation or the cities names are processed in another way now or something completely different.

Will upload a logfile with many errors to main thread soon. Maybe there is sthg usable in.