Cornelis Ariensz van Velsen (geb. ca. 1680, ovl. 1716) is married to Maria Leendertsdr Noordermeer 25-10-1706 in Berkel (link). He is assisted by his father Arij Cornelisz van Velsen. Arij in Zoetermeer / Zegwaart is his father and he is married three times:

1. 23-10-1674 in Leiden to Jannetje Willemsdr van Parle (link)
2. 21-12-1686 in Zegwaart, as widower of Jannetje Willemsdr Pluijmgraeff, to Marijtje Ariensdr Roskam (link)
3. 31-1-1692 in Bleiswijk, as widower of Marijtje Ariensdr Roskam, to Maertje Pietersdr (Maertje Pietersdr is a witness to multiple 

Unfortunately  can find only one baptism for Catharina, daughter of Marijtje Roskam in Zoetermeer on 30-11-1687 who is married to Frans Ariensz Verburgh in 1719 (she is possibly referred to as 't Hooft here). Arij has at least one other daughter, Marijtje who is married to Albreght Ariensz Boer in 1718 and has several children christened in Berkel witnessed by Maria Noordermeer (demonstrating that Cornelis, Marijtje and Catharina are indeed all siblings).

Given the timing of Catharina's birth, and that Cornelis marries in 1706 it seems his mother must be Arij's first wife, Jannetje. She is referred to as both "van Parle" and "Pluijmgraeff." I am not having much luck finding either Arij's parents, or Jannetje's, but there is one interesting notarial record which may refer to her father. It is recorded in Leiden in 1620 and includes "Willem Dircksz Jonge Pluijmgraeff." I have trouble making out the names, but it concerns a "(?) Dircksz, Pluijmgraeff van (?)burg" and can be found here (link).

The notarial record is about Willem Dircxsz Jonge Pluijmgraeff, who went to East Indie with a ship called " d' Orangieboom". Dirck Dircxsz Jonge Pluijmgraeff and Gijsbrecht Dircxsz Jonge Pluijmgraeff [his brothers?] also went to East Indie.

The deed is a power of attorney bij Dirck Dircksz Pluijmgraeff from Valkenburg, for himself and in the name of his children Willem, Dirck and Gijsbrecht. Apparently they still had wages coming to them from their trip to Oost-Indië.

No doubt you've noticed that there is quite some time between this deed in 1620 and Jannetje marrying in 1674.

You may find Arij Cornelisz van Velsen a couple of times in the notarial deeds of Zoetermeer < LINK > . At first glance, it doesn't look very interesting, but who knows. 

Regards, Frans

I did find it unlikely given the time difference, but as far as I can tell it's the only (indexed) reference to a Willem Pluijmgraaf and it seemed at least a hint. There does seem to be a concentration of the family name around this time in Katwijk, but nothing I can find that would connect them. The "van Parle" name is interesting, but again comes up with very little. Given it seems to have a French root, maybe we are dealing with a recent immigrant.

There seems to also be a strong concentration of the Parlevliet name in the Katwijk area today (link). That overlaps with the concentration of Pluimgraafs in the area. Not a lot to go on, and no Willem Parlevliets found yet, but it's something.