Saying "heighth" is just an old southern way of saying height. It's the same way someone says "oral" instead of "oil" or mispronounces Cincinnati or Missouri as Cincinnat-uh or Mizzour-uh. It's not meant to be a new word, just a mispronunciation of an existing word.
For what it's worth...
I don't know of anyone who "says 'oral' instead of 'oil' "
I grew up in rural Kentucky and many people say...um..."ohl"...rhymes with...well...I can't think of any rhymes.
When Dennis Doyle became MLB player Denny Doyle (pronounced Doyal), the announcers pronounced it differently than we townfolk had always pronounced it.
Same with his younger brothers. They were the Doyle twins (pronounced sort of "dohwl") twins. Then when Brian played for the Yankees, he became Brian Doyle (Doyal).
And I grew up pronouncing those guys on the Reds as playing for Cincinnat-uh.