i found this quote of Catherine Radziwill from "The Royal Marriage Market of Europe" in Wikipedia. Maybe it could be useful
"Prince Eitel Fritz, who is his father's favourite, being as tall as he is brutal, and as ferocious as he is fat, took to himself a wife almost by compulsion, and in order to put an end to ugly rumours that were flying about Berlin concerning him and his strange propensities"
If this is true i had no idea he was Wilhelm`s favorite son.