vital records sources
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Hannah was born in Lynn, Massachusetts Bay Colony, and moved to what is now downtown Salem after she married. There's no record of her death or good evidence of about when it happened, but Widow Hannah King was given a license to run and inn and sell liquor in 1720.1 She may have been Hannah (King) Bacon.
     The only birth record among her children is for the last: Benjamin in 1716.2 There is a baptism for son Samuel in 17143 and a group baptism for her first four children in 1712.4 Among the children, evidently four married but only Tabitha had children of her own. Hannah, Jr., the oldest, undoubtedly married Joseph Hilliard in 1722.5 Thomas Baldwin, in his Bacon genealogy,6 may have been the first to say this was a second marriage of her widowed mother, which seems to have legitimized the thought for later researchers. Baldwin calls him "Willard," probably because of a slip of the pen in one of the early record transcripts and that it appears just before the marriage of a man named "Willard." Despite the handwriting anomoly, those records show it was "Hillard" and certainly not "Willard." Process of elimination shows that he was the Joseph Hilliard (variously spelled) born in Salem in 1700.7
     Baldwin may also have let the 1712 baptism date for the four oldest children obscure his reasoning when he says Hannah, Sr., married "Willard." If there were about two years between the births of those four children, the first was born about 1703-1705. Their parents were married in January 1702 (not 1701, which is a mistake many people have made by not transcribing from the Julian to Gregorian calendars), and Hannah could have been born later in that year or in 1703, making her either 19 or 20 years old in 1722, the year of the Hillard marriage. Aside from this, it's not reasonable in the early 18th century to think widow Hannah, in her early 40s, would marry a 22 year old single man. "Joseph Willard" was an otherwise unknown man, so this disparity wasn't a factor for Baldwin.
     John, who was likely the second-born child probably died young. Tabitha was likely the third-born. Her gravestone says she died on 7 March 1785 at age 66.8 If correct, this puts her birth between 7 March 1708 and 7 March 1709. Mary's death record says she was also 66 when she died on 30 June 1778,9 making her the likely fourth child baptized in 1712 and putting her birth between 30 June 1711 and 19 June 1712, the day before the baptism.
     When John died he left Hannah with at least four, maybe six, young children. John's estate was insolvent due to massive debts, so it was common for a widow in those circumstances to remarry, but there's no plausible evidence that she did.

children of Hannah King and John Bacon:

children of Hannah King and John Bacon. John, Hannah or both must have joined the First Church of Salem about 20 July 1712, since the first four of their children were baptized there on that day:

1. Hannah, b. abt 1702-03, bap. 20 July 1712, m. Joseph Hilliard, 1722, no further record
2. John, b. abt 1705, bap. 20 July 1712, no further record
3. Tabitha, b. 1708-09, bap. 20 July 1712
4. Mary, b. abt. 1712, bap. 20 July 1712, m. 1. Benjamin Stacey, 25 September 1735, Salem, 2. Josiah Orne, 28 December 1771, Marblehead10
5. Samuel, bap. 29 August 1714, bricklayer in Boston 1735, when, as son of John of Salem, he sold his right to his grandfather Daniel Bacon's estate, no further record, didn't marry Mary Pickering (see Bacons of Dedham/Needham)12

vital records sources: The marriage of Hannah King and John Bacon appears in The Vital Records of Salem, Massachusetts, to the End of the Year 1849, vol. 3 (Salem: Essex Institute, 1924), 571.

1.
2. The Vital Records of Salem, Massachusetts, to the End of the Year 1849, vol. 1 (Salem: Essex Institute, 1916), 60-61, corroborated in the First Church of Salem records at the Congregational Archives & Library website.
3. Ibid.
4. Ibid.
5. Ibid, vol. 3 (Salem, MA: Essex Institute, 1924), 69.
6. Bacon Genealogy, Michael Bacon of Dedham, 1640 and His Descendants (Cambridge, MA: 1915), 123.
7. Ibid, vol. 1 (Salem, MA: Essex Institute, 1916), 434.
8. Vital records of Marblehead, Massachusetts, to the end of the year 1849 (hereafter VRM), vol. 2 (Salem, MA: Essex Institute, 1908), 593.
9. Ibid, 625.
10. VRM, vol. 2 (Salem, MA: Essex Institute, 1908), 403.
11. Essex Co., MA, deeds, 72:268.
12. VRM, vol. 2, 18.