Deliverance was the son of Lt. John Smith, who first appeared in Plymouth ca.1629 as a servant of the Mayflower passenger Edward Doty. He is referred to as John Smith "Jr." but in those days Jr. could refer to the younger of two people of the same name, it doesn't necessarily mean they are related. In 1660 he was fined for allowing Quaker meetings at his house. In 1665 he removed to Dartmouth. In 1674 he was appointed Lieutenant for Dartmouth (in those days the Quakers weren't as fastidious about bearing arms as they were later to become). He married, first, Deborah2(Arthur1) Howland, he married second Ruhamah2(Richard1) Kirby.
Deliverance Smith was elected a selectman in 1708 and was imprisoned for refusing to collect the tax for a "hireling minister" (i.e. a Puritan/Congregational minister, which the predominantly Quaker settlers of Dartmouth had no use for). His daughter Hope Smith b. 23 Nov. 1703 m. 20 Dec. 1729 Thomas Briggs. My source, Malathiah Dwight's "Kirbys of New England" has another daughter, Abigail Smith b. 10 Feb. 1709 also marrying a Thomas Briggs. It was fairly common in those days for a widower to marry a sister of his first wife, maybe that's what happened here.