John Ayer/Eyer of Haverhill, MS is most probably not the son of Thomas and Eliz Rogers. His wife was not an Evered alias Webb, but her first name is corectly Hannah.
The John who married Susan Symonds was of Ipswich. His name is most often recorded as Ayres. This man was killed by Indians at Brookfield Massachusetts.
John Ayer, son of John and Hannah of Haverhill, married Sarah Williams; she died in May 1646. He married second Mary Wooddam.
John Ayer, son of John and Sarah, married Mary, whose maiden name I did not find. This man lived in Andover Massachusetts and died there before 23 September 1683. His widow is probably the Mary Ayer who married Ephraim Davis at Andover on 19 March 1688.