Elisabeth (Kobi) Conaway, daughter of Ernst Kobi and Klara Merz, immigrated to the U.S. The family has no further information.
According to the Swiss Historic dictionary, there was Kobi families in two swiss municipalities prior to 1800 :
Note that both of those places are almost neighbouring, so the most likely is that the "nest" of Kobis came from here, and then they went living elsewere in Switzerland.
In 1949, a Kobi family bought the bourgeoisie (just to be clear, this has nothing to do with marxism) in Wintertur, but that family was originally from Rapperswil (BE). Back then the rules for having bourgeoisies were set high, so it's very likely the family was living in Wintertur since a long time.(*)
Merz is a very common name so it could be from almost anywhere.
(*) For example my own family bought the bourgeoisie in a municipality in 1947(**), but they lived there since 1920.
(**) a fact I also learned thanks to the Swiss Historic Dictionary