Apparently it's from the old French spelling.
av·oir·du·pois ( P ) Pronunciation Key (vr-d-poiz)
n.
Abbr. av. or avdp. Avoirdupois weight.
Informal. Weight or heaviness, especially of a person.
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[Middle English avoir de pois, commodities sold by weight, alteration of Old French aveir de peis, goods of weight : aveir, avoir, to have (from Latin habre. See able) + de, of (from Latin d, from. See de-) + peis, pois, weight (from Vulgar Latin *psum, from Latin pnsum, past participle of pendere, to hang. See (s)pen- in Indo-European Roots).]