In a note about Stephen, "the third of that name in this family," the 1629 Roberts pedigree contends that "the proofe" of this marriage "is shewed in a deede dated the
ffryday next before the ffeast of St. Hyerome in the third year of King Richard the
Second," and relates the contents of the deed as, "that deed conteyning that John Nywmanne of Cranebrooke did grant to Joane wife of Stephen Roobertes of Gowdhurst some tyme the daughter of William Tillye of Cranebrooke and to the heirs begotten between the said Stephen and Joane all the lands in Cranebrooke which the said Nywmanne had of guift of the said William Tillye"  A nearly identical explanation appears in the 1592 pedigree.  The feast day of St. Jerome is 30 September, and the preceding Friday in 1379 was 23 September.
The Roberts pedigree in Hovenden, Visitation of Kent, includes, as the second of six quarters, arms attributed to "Tillye" in the 1592 and 1629 Roberts pedigrees, but does not show the Tillye marriage. 
 Fane Lambarde, “Roberts of Kent,” Miscellanea Genealogica et Heraldica, Ser. 5, Vol. 6 (1926-1928), 168–187 at 183, [FHLCatalog].
 William Hayley, “Sussex: viz. Genealogica, Vol. II” (British Library Add. MS 6347), fol. 1–6, of which folios 2-5 and the front of fol. 6 are numbered in Hayley's hand as pages 1-9 and provide a transcription of a pedigree, dated 1592, of the Roberts family of Glassenbury), 2.
 Robert Hovenden, ed., The Visitation of Kent, taken in the Years 1619–1621, Publications of The Harleian Society, Visitation Series, Vol. 42 (London, 1898), 93-94, [GoogleBooks].