Origin of "height"

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.