Middle English word heih comes from Proto-Indo-European *kow-, and later Proto-Germanic *hauhaz (High.)

Detailed word origin of heih

Dictionary entry	Language	Definition
*kow-	Proto-Indo-European (ine-pro)
*kūk-	Proto-Indo-European (ine-pro)
*kew-k-	Proto-Indo-European (ine-pro)
*kówkos	Proto-Indo-European (ine-pro)
*hauhaz	Proto-Germanic (gem-pro)	High.
hēah	Old English (ang)
high	Middle English (enm)

Words with the same origin as heih