I'm just amazed about all that's to be found on the Balsigers! Here's my two cents worth (told to me by my late grand father Ernst Balsiger, born 1908).
The name Balsiger originates from the two words Palme (palm tree) and Sieger (winner). Apparently, some branch of the Balsigers used to be merecenaries and regularly winning competitions where the first pricze was a branch of a palm tree. According to my grandpa, Palmensieger (winner of the palm) became Balsiger. For this reason, the family banner that has been handed down through my branch has apalm tree in it (flanked by two stars).
Does anybody know if this is true?