Heighth is a colloquial variant of height formed by analogy with similar measurement terms such as length, breadth, width, and depth, which end in th. Heighth might be considered incorrect in formal writing, and no dictionaries that we know of list it as a living word. Its use is a common peeve among people who consider themselves careful users of English.
But those who are peeved by heighth should go easier on it. It is not just a new colloquialism. It was in fact the Old and Middle English term for the quality of being high for many centuries (under various spellings) before height entered the language in the 16th century,1 and the newer form didn’t achieve its modern prevalence until the late 19th century.2
Plus, since so many measurement terms end in th, the much-maligned modern use of heighth is really just a normalization. We don’t have to consider it correct or use it ourselves, but its use is perfectly logical and is not a sign of low intelligence or illiteracy.
Here are a few examples of heighth used in current writing:
West Virginia’s aggressive defense and heighth took over from there. [The Daily Athenaeum]
Nearly two feet of snow fell in New York City and winds blew at nearly 60 mph at John F. Kennedy International Airport at the heighth of the storm. [Omaha World-Herald]
They’re not incredibly tall; they’re like us heighth-wise, so it should be a pretty good matchup. [Waterloo Cedar Falls Courier]
In our searches, heighth appears most often in sportswriting. And in our own experience, use of the the word seems endemic in TV sports commentary.