A lot of research has been done on this and nobody's been able to figure anything about the origin of this surname. There are no Yeargins or Yeargains in England. According to the information at
http://freepages.genealogy.rootsweb.ancestry.com/~yearg/Welcome.html, there's no evidence that the first bearer of the surname in the US came from Wales.
It's been proposed at
http://www.ancestry.com/name-origin?surname=yeargin that the origin is German Jürgen but that's pure speculation.