This is one of the 117 mis-spellings listed as 'Common difficulties' in the section on 'Spelling' within 'Writing' in UEfAP.
The abstract noun height is spelled thus.
McArthur (2005) points out that "Common misspellings include confusion over silent letters (for example, 'figth' for fight)" (s.v. English spelling, in Spelling). Some difficulties with height may be
- because it is derived from the adjective high, which has no '-e-'
- the combination of letters '-eigh-' is more usually the spelling of the /eɪ/ sound, as in eight (8) and weight.
- height was, until the eighteenth century, commonly written with what we now see as an extra '-h': heighth, using the common Germanic suffix '-th' to form a noun from an adjective, as in the words of measurement depth (from 'deep'), width (from 'wide'), length (from 'long') and breadth (from 'broad').
- Other nouns formed in this way from adjectives include health ('hale', modern 'whole'), filth ('foul'), youth ('young'), wealth ('weal', or 'well'), warmth ('warm') (and the mostly jocular coolth, from 'cool') and mirth ('merry'); and from verbs death (from 'to die'), birth ('to bear'), stealth (from 'to steal', mostly in the sense 'to move secretly or surreptitiously'), growth ('to grow') and tilth ('to till')