Old English becweðan "to say, speak to, exhort, blame," also "leave by will;" from be- + cweðan "to say," from Proto-Germanic *kwithan (see quoth). The simple verb became obsolete, but its old, strong past tense survived through Middle English as quoth.
The original sense of "say, utter" died out 13c., leaving the word with only the legal sense of "transfer by legacy." Compare bequest. "An old word kept alive in wills" [OED 1st ed.]. Old English bequeðere meant "interpreter, translator." Related: Bequeathed; bequeathing.