'height-associated' is a compound formed from the English noun 'height' and the adjective 'associated'. 'height' originates from Old English 'hēah' meaning 'high'. 'associated' ultimately comes from Latin 'associare' (from 'ad-' + 'socius') meaning 'to join or unite with'.

'associated' came into English via Latin 'associare' and Old French/Medieval Latin forms (e.g. Old French 'associer', Middle English 'associate'), and the compound construction combining a noun with a past-participial adjective (e.g. 'height-associated') is a modern English formation used to describe correlation or linkage.

Initially, 'associate' and its derivatives meant 'to join or unite'. Over time, derivatives like 'associated' have been used more broadly to indicate linkage or correlation; the compound 'height-associated' specifically came to mean 'linked or correlated with height'.