There is a Richard Justice who was MP 30 years after Wm and Mayor in 1539 and 1545 and had his will proved in 1549.  Might he have been Wm's son?  Richard also appears in various church registers.

In the Berks 1532 Visitation there is an entry that says that Thomas Vachell of Colley, Berks married "Annes doughter of Wm Justice of Redding in the Count of Barkshir and hath yssue by her Thomas, Elisabethe Mary briget and Margret".  I wonder if Annes was a/the co-heir of this Wm Justice?  This account is repeated in the 1556 Visitation., but with no further identification of the Wm Justice.  And a repeat in the Berks visitation of 1623, still no further identification.

Also in the Berks visitation, Vol II, p. 160, is a Mary Justice, dau & heir of Wm Justice of Reding, Barks, wife to John Yate(s) of Lyvorde, Berks and she was granted arms of:
Argent on a fesse engrailed sable three crescents or between three turtle doves proper beaked and membered gules and holding in every beak a marygold stalked and leaved vert.

And there is a note that Thos Justice of Reading, clerk of the law, had the arms:
Or, between two barrulets sable, on a fesse engrailed sable  three crescents or.
His will was proved in 1536.
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April 2003: In the Norfolk Visitation of 1664, Vol 2, p. 254, there is a Joan Justice, dau. of Rich. Justice of Reading, who died at Chigwell, Essex in 1568, having married Robert Browne of Leisten, Suffolk, Baron of the Exchequer in 1550, who died in 1559.
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July 2008, TFPL: Additionally, to confirm the above Berks 1552 visitation, Burke’s Extinct Baronetcies has an entry for Sir Edward Yate, 1st baronet in 1622, who was (a) gt-grandson of William Justice and (b) gt-gt-grandson of John Yate of Charney whose daughter Anne m. John Latton of Chilton and which Anne then had a dau. Margaret who m. Tipping.
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Jul 2008, TFPL: I have found, by going throughly through the index, this entry of a wife to a William Justice of Reading:

1566 visitation of Berks, p. 43 for Martyn of Ockingham: “Alyce married to William Justice of Reading in com Berks”.  Alice was eldest (probably) dau. of John Martyn who was the father of William Martyne the apparent subject of the visitation.  This William had married twice and even the youngest dau. of the second marriage was married; this indicates William was at least 50 and thus his sister Alice was much the same, thus born 1500 to 1516 or so.  This looks like a bit young to have been the mother of Bridget Justice whose eldest son, probably not her firstborn, was born in 1525.
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Nov 2010: Claire nash has written with this information:

“Richard Smyth, of Redyng, Berks, and London, g. or clothier, and Agnes
his wife, late the wife of Henry Justice, 26 May. 1509. (Pardon Roll,
Henry 8, in British History Online)

“For more on Smyth see Bindoff, House of Commons which states that
Henry's heir was Richard Justice.

“Henry Justice along with London/Reading merchants Yonge (Yong, Young)
and Richard Smyth held land next to the abbey of Reading. ”
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Harl MS 1532, fol 55, gives these arms with the note: Thomas Justice of Reading, Clarke of the law, 1526:

Or on a fess engrailed sable three crescents of the first.
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Or on a fess engrailed sable three crescents of the first.

Berks vis’n of 1532-1666, vol II, p. 160; Vincent 161/2..

Harl MS 1532, fol 55, gives these arms with the note: Thomas Justice of Reading, Clarke of the law, 1526.