'well-addressed' originates from modern English, formed by combining the adverb 'well' and the past participle of the verb 'address'.

'address' comes from Old French 'adresser' (to direct, arrange), which in turn derives from Latin roots related to 'ad-' (to/toward) and a form of 'directare'/'directus' (to direct). The compound sense combining 'well' + past participle arose in English by productive use of 'well' with past participles to mean 'properly [past action]'.

Initially, 'address' carried senses of directing or speaking to someone; over time the past participle came to be used adjectivally to mean 'dealt with' or 'treated', and 'well-addressed' specifically means 'dealt with properly'.