Please forgive me for intruding on this conversation.
The will of Simon Welbury (Symon Welberye of Castle-Eden), dated 13 Aug 1581 and probated 1583, can be found in _Wills and Inventories from the Registry at Durham_, vol. 3 (Surtees Society vol. 112) (Durham: 1906), pp. 87-88, viewable at
https://archive.org/details/willsandinvento00woodgoog/page/n98/mode/2up. This will indeed lists a granddaughter Margery, daughter of his son Anthony, but unfortunately without last or married name.
I did not find a reference to Welbury in vol. 1 of the Surtees county history published in 1908; perhaps I was not looking in the right place. And I also did not find a reference on p. 185 of the Hartlepool section, published in 1910; though on p. 184 it does mention that in 1553 Simon Welbury and Christopher Morland, among others, were granted four messuages with their appurtenances in Wingate (no reference, as far as I can tell, to Simon's son or granddaughter).
I believe the reference to the Welbury pedigree in _The History and Antiquities of the County Palatine of Durham_ you want is the pedigree on p. 57 of vol. 3 of the 1908-1910 edition, which can be seen at
https://archive.org/details/historyantiquiti03surt/page/56/mode/2up. This indeed shows John Eden as wife of Margery, granddaughter of Simon Welbury, but doesn't state explicitly on what evidence this is based. The only date listed for Margery is 1583, which is a reference back to the will of Simon Welbury probated that year (the same date is listed for a number of other people in the pedigree). For John Eden it states "ob. 1588"
I have also located the family history, which is Robert Allan Eden, _Some Historical Notes on the Eden Family_ (London: 1907). This appears to be not available through Google, but is available (behind a paywall) at
ancestry.com (at
https://www.ancestry.com/imageviewer/collections/17835/images/dvm_GenMono003631-00001-0). According to p. 22 of this publication, the John Eden who married Margery Welbury, daughter of Anthony Welbury of Castle Eden, was the John Eden born 1571, grandson of the John Eden who died 1588.
The only evidence given by the Eden family history for John Eden's marriage to Margery Welbury is a reference to Surtees Society Publication vol. 34, pp. 44-48. This publication is _The Acts of the High Commission Court Within the Diocese of Durham_ (Edinburgh: 1858). On pp. 44-48 (viewable at
https://archive.org/details/actshighcommissi34surtuoft/page/44/mode/2up) is considerable witness testimony in the 1633 case of Marie Daniell, spinster, for having committed adultery with John Eden, esquire, and having alienated his affection from his wife. On p. 45 an editorial footnote identifies this wife as "Margaret, daughter of Anthony Welbury of Castle Eden," but gives no source for this identification, and I see no mention of her actual name in the witness testimony.
Thus, at least from what I have seen so far, we do have contemporary evidence that Simon Welbury had a daughter Margery, but the evidence of her husband is conflicting, with a late-18th century pedigree asserting her husband was the John Eden who died 1588, while a mid-1850s editorial comment asserts her husband was the John Eden who was still alive (and living in sin) in 1633.