This one surprised me, although the clues were there (eg naive, naif). Waive comes from Anglo-Norman weyver, which is a dialect variation of Old French gaiver, “to allow to become a ‘waif’, to abandon”.
The initial sense in English is (from OED):
1. trans. Law. To deprive (a person) of the benefit and protection of the law as a punishment; to outlaw. Chiefly in pass.In Anglo-Norman weyver had the sense ‘to abandon, disclaim ownership of (a serf)’: see Britton i. xxxii. §8.
†a. gen. = outlaw v. Obs.
1297 R. Gloucester’s Chron. (Rolls) 10823 He let al so uor is loue deliueri of prison Sir hubert de boru & oþere þat in prison were ido & hom þat iweiued were is pes he ȝef al so.
Hence through various related senses to the modern meaning.