ITEM 1: Piperne vs. Pimperne
I don't know what "Piperne" is/was unless it was Ye Olde Enlglish spelling for Pimperne...about 28 miles from Weymouth. I believe each place was distinctly different then and not bound into one parish.
– https://www.familysearch.org/en/wiki/Pimperne,_Dorset_Genealogy
– https://www.familysearch.org/en/wiki/Weymouth,_Dorset_Genealogy
ITEM 2: Daughter Lydia
– I'm not convinced that Lydia was a daughter of William and Sarah unless the snags below find resolution:
Snag A: Lydia's profile shows "Birth: 1585 London, England"
Snag B: If Sarah was her mother, she would have been about age 13—in London when she gave birth. This seems nonsensical given that Sarah birth and death shows as occurring in county Dorset.
Snag C: Lydia's death shows "1685 Henrico, Virginia".
Snag D: Therefore, she apparently was an immigrant landing near Virginia and didn't emigrate from England with supposed brother, William II.
– The last two points might make sense if Lydia was Not born in London. Also, if one or more sources show her birth in 1585, then her mother's circa birth year being adjusted closer to that of her husband's birth might be valid.
ITEM 3: Daughter Mary
I'm not sure if Mary was a daughter of William and Sarah given data presently appearing.
– Mary's profile shows a 1592 birth in "Axminster, Devon, England".
– William and Sarah lived/died near to Weymouth, Dorset.
– Axminster is 35 miles from Weymouth and 48 miles from Pimperne.
SIBLINGS: Master Profiles for William II, Tomasine, and Hannah all show births in Weymouth.