Height
Old English hēhthu (in the sense ‘top of something’), of Germanic origin; related to Dutch hoogte, also to high.
wiktionary
From Middle English heighte, heiȝþe, from Old English hēahþu, hēhþo, hīehþo(“height”), Proto-West Germanic *hauhiþu, from Proto-Germanic *hauhiþō (compare *hauhaz). Corresponds to high + -th.
etymonline
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.
