Said to have a daughter, Bridget ("BATEMAN") BROWN, but no such child is mentioned in our subject's will.  This Bridget is said to have been born in Hawkedon, SFK, so the geography argues against the connection as well. 

1.  Clarence Almon Torrey.  1997.  New England Marriages Prior to 1700.  Genealogical Publ. Co., Baltimore, MD:

p. 52	BATEMAN, William ( -1658) & __?__; b 1615; Concord/Milford, CT / Fairfield, CT
p. 52	BATEMAN, Thomas (1615-1669) & 1/wf Martha [BROOKS], dau Henry; b 1638?, b 1645; Concord, MA
p. 507	MIDDLEBROOK, Joseph1 (-1686) & 1/wf __?__ [BATEMAN]; b 1650; Fairfield, CT

The "b 1615" and "b 1650" refer to the birthyear of the first known child, as an indicator of approximate year of marriage.  Locations are the husband's known residences, ending with his place of death.  Brackets indicate the source is something other than a marriage record.

2.  Louis F. Middlebrook.  1909.  Register of the Middlebrook Family.  Self-published, Hartford, CT (Broderbund CD-117). On p. 21 (boldface added):

p. 20	18 Jann 1649 Granted to Jofeph Midelbrook from the Towne... Alfoe one parcell of land in the feald called Concord feald contayning two acres more or leff founded on the north weft with the hieway on the northeaft with the land of William Bateman on the Southeast with the creek on the South west with the land of James Bennitt... 20 May 1656 Jofep melbrok had granted to him from the town a parfell
p. 21	of upland contayning four acres and half mor or les lying on the eaft sid of Unckaway River bounded on the South with a highway on the eaft with ye land of anthony willfon: on the north with the comon: on the weft with the land of William bateman.

The "town" referred to is Fairfield, CT.

3.  Donald Lines Jacobus.  1930-32.  History and Genealogy of the Families of Old Fairfield.  Fairfield, CT (reprinted 1976/91 by Genealogical Publ. Co., Baltimore; Broderbund CD-515).  On p. 38:

Bateman, William.   He was of Concord, freeman 1641; rem. to Fairfield, presumably with the Jones party.   Will 24 Mar. 1656; one-half to son Thomas, now of Concord; one-half to son-in-law Henry Lyon; except £5 to gr. child Joseph Joseph Middlebrook, under 18.  If Middlebrook dies, the £5 to be divided equally between Thomas and Henry.  Witnesses: Andrew Ward, William Ward.  Henry Lyon signed 27 Apr. 1657 a document now mostly illegible.  Will exhibited 20 Oct. 1658.   Children:     Thomas, of Concord, b. abt. 1615, d. 6 Feb. 1668/9 ae. 54; m. Martha _____.     Daughter, m. Henry Lyon.     Daughter, m. Joseph Middlebrook.

4.  John Farmer.  1829.  Genealogical Register of the First Settlers of New England.  Carter, Andrews & Co., Lancaster, MA (republ. 1964/69 by Genealogical Publ. Co., Baltimore; online at GenealogyLibrary.com).   On p. 351:

To the following persons may be added or corrected the year of their admission as freemen of the Massachusetts Colony... Bateman, William, 1642...

5.  James Savage.  1860-62.  A Genealogical Dictionary of the First Settlers of New England.  Little, Brown & Co., Boston (reprinted 1965, Genealogical Pub. Co., Baltimore; online at GenealogyLibrary.com).  Section on Bateman on pp. 90-91.  William mentions his son, Thomas, his son-in-law, Henry Lyon, and the grandchildren of Joseph Middlebrook in his will. 

6.  Broderbund.  World Family Trees.