height: [OE] Etymologically as well as semantically, height is the ‘condition of being high’. It was formed in prehistoric Germanic from *khaukh- (source of high) and *-ithā, an abstract noun suffix: combined, they came down to Old English as hēhthu. The change of final -th to -t seems to have begun in the 13th century. The spelling ei reflects the word’s pronunciation in Middle English times, when it rhymed approximately with modern English hate. => high
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. 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. The modern pronunciation with -t emerged 13c., but wasn't established till 19c., and heighth is still colloquial.