French, avoir, aver or avier, goods in general, and poise = poids (weight). Not the verb, but the noun avoir. Properly avoir de poids (goods having weight), goods sold by weight. We have the word aver, meaning goods in general, hence also cattle; whence such compounds as aver-corn, aver-penny, aver-silver, aver-land, and so on. We have also the noun “having, havings” = possessions.
There is a common French phrase avoir du poids (to be weight), with which our word avoir dupois has been muddled up.
Pared my present havings [property] to bestow My bounties upon you.
“One of your having, and yet cark and care.”
Even medicines, as wholesale goods, are bought and sold by avoirdupois weight.
Source: Dictionary of Phrase and Fable, E. Cobham Brewer, 1894