With respect to the male-line ancestry of Richard Belasyse, I've seen three different versions, in Collins' Peerage (Bridges ed.), Burke's Extinct Peerages, and Foster's ed. of the Yorkshire Visitations. I'm inclined to favor the Collins version, as it's much more detailed and provides at least some sources - but I'm open to differing thoughts.
In the condensed versions below I've used the surname Belasyse, although one source (Foster) spells it Bellasis. Note that the given names of the Belasyse men and their wives are sometimes different between the versions, in addition to the differences in relationships. I've started with the earliest generation in Leo's post - all three versions have several earlier generations and are consistent in these.
Collins' Peerage (Bridges ed.), vol. 6:
1. Sir John Belasyse, m. Oswald Talbois
2. John Belasyse, m. Alice de la Hay
3. William Belasyse, m. Maud Bellingham
4. Sir John Belasyse, m. Alice Hansard
5. Robert Belasyse, m. Alice Lamplugh
6. William Belasyse, m. Cecily Hoton [or Hutton]
7. Thomas Belasyse, m. (2) Margaret Thirkeld
8. Richard Belasyse, m. Margery Errington
Burke's Extinct Peerages:
1. Sir John Belasyse, m. Oswald Talbois
2. John Belasyse, m. Alice de la Hay
3. William Belasyse, m. Maud Bellingham
4. Sir John Belasyse, m. Alice Hansard
5. Robert Belasyse, m. Alice Lamplugh
6. William Belasyse, m. (2) Margaret Thirkeld
7. Richard Belasyse, m. Margery Errington
Foster's Yorkshire Visitations:
1. Sir John Belasyse, m. Oswald Talbois
2. John Belasyse, m. Alice de la Hay
3. William Belasyse, m. Maud Bellingham
4. Sir John Belasyse, m. Alice Hansard
5. John Belasyse, m. Anne Lamplugh
6. William Belasyse, m. Jennett Tipping
7. Thomas Belasyse, m. (3?) Margaret Thirkeld
8. Richard Belasyse, m. Margery Errington
I'll try to comment on some of the other families mentioned by Leo in separate posts.