The proper spelling, of course, is height. Yet because many people improperly pronounce the word with an ending ‑th, you’ll sometimes see the word heighth. In the Richmond Times Dispatch, we see this error:
Second-seeded Syracuse had intermittent difficulties with No. 15 Coppin State’s zone defenses, but Syracuse’s heighth and strength won out. Quoted in Garner, Oxford, p. 168.
The mistake probably arose because of other “size and distance” words with ‑th endings: width, depth, and breadth. But whatever its origins, heighth does not enter the language of good writers and speakers.