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According to Etymonline, Height, has many different possible origins.

height (n.) Old English hiehþu, Anglian hehþo "highest part or point, summit; the heavens, heaven," from root of heah "high" (see high) + -itha, Germanic abstract noun suffix (as in width, depth; see -th (2)). Compare Old Norse hæð, Middle Dutch hoochte, Old High German hohida, Gothic hauhiþa "height." Meaning "distance from bottom to top" is from late 13c. Meaning "excellence, high degree of a quality" is late 14c. Century Dictionary says "there is no reason for the distinction of vowel between high and height. The modern pronunciation with -t emerged 13c. but wasn't established until 19c.; Milton used highth and heighth is still colloquial in English. Compare Dutch hoogte, Danish hjöde.

What is the correct and definite origin of Height?

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    The full (subscription-only) OED etymology starts with Old English híehþo (also later héahþu ) = Old Low German *hôhitha (Middle Dutch hogede , hochte , hoochte , Dutch hoogte , Middle Low German hogede , Low German högte ), Old High German hôhida (Middle High German hoehede ), Gothic hauhiþa , < hauh- high n.1 + abstract ending -iþa : see -th suffix1. From the 13th cent. the final -th after -ȝ , -gh varied with t (compare drought , drouth ). In Middle English... I take it we're not much interested in the remaining 3/4 of that section. – FumbleFingers Dec 16 '15 at 17:30
  • The etymology you cite gives one origin only. Did you overlook the word "compare"? – phoog Dec 16 '15 at 18:21
  • As it's an OE word (more than 1200 years old) it will have accreted various influences including ON. I believe that the etymology you cite is the best you're going to get -- with the possible exception of OED, which says much the same thing. – Andrew Leach Dec 16 '15 at 18:32
  • For comparison, see heighth – Mitch Dec 16 '15 at 22:56
  • Old English (and modern English, for that matter) is a Germanic language, so the Germanic abstract noun suffix here was inherited normally. All of the languages mentioned in the entry are Germanic, in fact, and calling the suffix "Germanic" means it has a common origin between them, rather than many separate origins. – herisson Dec 16 '15 at 23:37
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If you read the Etymonline passage more carefully you will see that it offers only one origin: OE hiehþu representing the root morpheme underlying heah "+ -itha, Germanic abstract noun suffix". Hehþo is provided as an attested OE spelling considered to be a variant from the Anglian dialect; most OE texts are written in Wessex dialect, but after the Conquest Anglian dialects dominated subsequent development in the spoken language.

The words which the passage invites you to compare are neither sources of ModE height nor versions intermediate between the OE and the ModE but cognates which exhibit similar development from conjectured Proto-Germanic morphemes.

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