Katherine, 10 years old, was one of the four children of William Kinge listed as immigrating to America with the Hull Company in 1635. She was born in England in 1625and died in Aquebogue about 1691. Her father, William King was an English Puritan, aged 40 years, her mother Dorothy aged 34 when they sailed from Weymouth, Dorsetshire, England in March of 1635-6; bound for New England.
Katherine's siblings who sailed with the family were Mary aged 12, William aged 8, Hannah aged 6 and Samuel aged 2.
The King family settled at Salem, Massachusetts. Her father was made a freeman on May 26, 1636but was put under Puritan ban in 1637 because he identified himself with the Antinomians and took an active part in this religious controversy.
Katherine King married John Swayze before 1650 in Salem.on March 12, 1650.They moved from Salem to Southold, Long Island as early as 1658 and became members of the first church founded in Southold in 1650, pastored by Rev. John Younge. In 1669 they moved to Aquebogue in Suffolk County.
Children of Katherine (King) Swayze and her husband John Swayze:
John born in Southold in 1651; died in 1717; married Mary __?__. They had at lease one son, John who married Sarah Ramsey on January 1, 1707.
Joseph who was born in 1653 and died before 1717.
Genealogy of the Swasey Family by Benjamin Franklin Swasey - Privately Printed for Ambrose Swasey, Cleveland, Ohio 1910 - NEHGS Library Media Book page 33-36 (Second Generation, Southold Branch)
John 2 Swayze, planter or husbandman (John 1), b. prob. in England, about 1619. Emigrated with his father and his brother Joseph to Salem, Mass., 1640; d. in Aquebogue, Suffolk County, Long Island, N. Y., 1706. M. bef. 1650 in Salem, Katherine King, b. in England, 1625; d. in Aquebogue, abt. 1691; daughter of William and Dorothy King of Salem.
NOTE: Date is the date of death of her husband, John Swazey. Listed in William and Dorothy King and Three Generations of their Long Island Descendants - page 72:
Katherine, b. in England about 1625-26; m. before 3.12, 1650, John Swazey (Swasie, Sweezey), of Salem, Mass., and Southold, L. I., who d. 10 June 1692.
The "who" refers to John Swazey, not Katherine King
William and Dorothy King, of Salem, Mass., and Three Generations of Their Long Island Descendants - compiled by Lucy Dubois Akerly from the Manuscript Genealogy of Rufus King of Yonkers, N. Y. (New York Genealogical and Biographical Record (NYGBR) from American Ancestors, Vol 33 April 1902, p. 72-73)
Katherine, daughter of William King and his wife Dorothy, born in England about 1625/6.
Katherine married before March 12, 1650 to John Swazey (Swasie, Sweezey) of Salem, Massachusetts and Southold, Long Island, who died June 10, 1692.
Children of Katherine (King) Swazey and John Swazey: John, Joseph, Samuel, Abigail who married John Hallock, Mehitable who married Peter Aldrich, Sarah, and Mary, all of whom are mentioned in their father's will.
Robert Charles Anderson, The Great Migration, Immigrants to New England, 1634-1635, I-L, Boston, MA: New England Historic Genealogical Society (2007), IV:  Digital copy from www.AmericanAncestors.org subscription site. Accessed 1 Oct 2016.
New York Genealogical and Biographical Record. (NYGBR) Online database AmericanAncestors.org, New England Historic Genealogical Society, 2011. William and Dorothy King and Three Generations of their Long Island Descendants. Vol. 33. p. 72-73.
Swasey, Benjamin Franklin of Exeter, New Hampshire. Genealogy of the Swasey Family Privately Printed for Ambrose Swasey, Cleveland, Ohio. 1910. p. 33 - 36. (Second Generation, Southold Branch). 
Katherine was born in England in 1625. She was the daughter of William and Dorothy King of Salem, Massachusetts. She married John Swazey in Salem and they moved to Southold on Long Island shortly after. She died in 1692 in Aquebogue, Suffolk County, New York.
↑ Robert Charles Anderson, The Great Migration, Immigrants to New England, 1634-1635, I-L, Boston, MA: New England Historic Genealogical Society (2007), IV: page 174. Digital copy from www.AmericanAncestors.org subscription site. Accessed 1 Oct 2016.
↑ 3.03.13.23.33.4 The New York Genealogical and Biographical Record. (NYGBR) Online database AmericanAncestors.org, New England Historic Genealogical Society, 2011. "William and Dorothy King and Three Generations of their Long Island Descendants." Vol. 33. p. 72, 73.
Source: S-2047058666 Title: U.S. and International Marriage Records, 1560-1900 Author: Yates Publishing Publication: Online publication - Provo, UT, USA: Ancestry.com Operations Inc, 2004.Original data - This unique collection of records was extracted from a variety of sources including family group sheets and electronic databases.
Source: S-2047177890 Title: Ancestry Family Trees Publication: Online publication - Provo, UT, USA: Ancestry.com. Original data: Family Tree files submitted by Ancestry members.
"William and Dorothy King, of Salem, Mass., and three generations of their Long Island Descendants" Lucy Dubois Akerly April 1902. Page 494
"Genealogy of the Swasey Family" by Benjamin Franklin Swasey published Cleveland 1910 - NEHGS Library Media Book page 33
"The King Family of Southold, Suffolk County, New York 1595-1901" Compiled from public records, family papers and the manuscript King Genealogy of Mr. Rufus King of Yonkers, NY. by Lois Dubois Akerly, Newburgh, N.Y. published 1901. (Pages 12-13) 
"East Hampton History Including Genealogies of Early Families" compiled by Jeannette Edwards Rattray published 1953. King section - page 411 William 1 - ch. Katherine 2 b. England abt. 1625/6, who m. before March 12, 1650 John Swasy of Salem, Mass. and Southold, L.I. 
"Genealogical and Biographical History of the King Family" compiled by Major Hugh E. King published 1955. Page 8 and 10 Katherine King (2) born 1625 in England, died at Southold. Married on March 12, 1650 to John Swazey of Salem. Seven children listed. William H. Steward, Secretary of State, was a descendant of John Swazey and Katherine King.