OED gives both spellings and pronunciations

But there have long been social overtones to this usage, I think.

Dickens used this form in Hard Times – “ha worked sin I were no heighth at aw, in Coketown heer?”

Vocabula Review opines priggishly:

“Abuses of language abound, especially among those who speak and write uneducated English. Whereas people who aspire to write and speak the language well still maintain standards of speech and observe distinctions between words, the uneducated, like some juggernaut, massacre and obliterate. They slay nearly all that they say…

heighth. She's over 6 feet in heighth. USE height.
I am the same size as you in heighth. USE height.”

http://www.vocabula.com/VRApr00.htm

More factually neutral is this, from H.L. Mencken’s ‘The American Language’ (1921):

“In the days of the great immigrations,… were certain speech habits that the Irish brought with them—habits of pronunciation, of syntax and even of grammar. These habits were, in part, the fruit of efforts to translate the idioms of Gaelic into English, and in part, as we have seen, survivals from the English of the age of James I. The latter, preserved by Irish conservatism in speech came into contact in America with habits surviving, with more or less change, from the same time, and so gave those American habits an unmistakable reinforcement. The Yankees had lived down such Jacobean pronunciations as tay for tea and desave for deceive, and these forms, on Irish lips, struck them as uncouth and absurd, but they still cling, in their common speech, to such forms as h’ist for hoist, bile for boil, chaw for chew, jine for join, sass for sauce, heighth for height,….”

http://www.bartleby.com/185/16.html