Midway #1 actually started off on Concourse A back in 1979, using some former United gates. Eventually they grew to use the entire concourse, and in the early 1980s expanded onto Concourse B as well. In the mid-1980s they added the odd second-level jetways that required passengers to climb a small flight of stairs.
Southwest used two or three gates on Concourse A before Midway shut down in 1991. They didn't take over all of Concourse A until after the shutdown, and that was only after some competition with Northwest over who would get to use the gates.