The 61-year-old Democrat ran on his efforts to reverse some of West Virginia's chronic economic woes, the Charleston (W.Va.) Gazette reported.
Weeks, who came in second, is a former state senator who served in Vietnam.
Johnson -- a filmmaker, actor, and theatrical producer -- also ran for governor in 2004.
The Mountain Party is affiliated with the Green Party.
Celebrity Families of 2014 [PHOTOS]