1520s, "to promise," from Old French afiancier "to pledge, promise, give one's word," from afiance (n.) "confidence, trust," from afier "to trust," from Late Latin affidare, from ad "to" (see ad-) + fidare "to trust," from fidus "faithful," from PIE root *bheidh- "to trust, confide, persuade."
From mid-16c. especially "to promise in marriage." The earlier form of the word was affy (Middle English affien "to trust, have faith; have faith in" c. 1300), from Old French afier. Related: Affianced; affiancing.