Middle English (originally as a legal term relating to removal of the protection of the law): from an Anglo-Norman French variant of Old French gaiver 'allow to become a waif, abandon'
Waive and waiver should not be confused with wave and waver. Waive is a transitive verb that means ‘surrender (a right or claim),’ and waiver is its related noun, meaning ‘an instance of waiving’ or ‘a document recording such waiving’: he waived potential rights in the case by signing the waiver. Wave, as a transitive verb, means ‘move (one’s hand, or something in one’s hand) to and fro’: she waved the paper to get their attention. Waver is an intransitive verb that means ‘shake with a quivering motion’ or ‘be undecided about two courses of action’: the tall grass wavered silently; at the last minute, he wavered and said he wasn’t sure whether he should go.