I've been looking through Ancestry, Findmypast and Familysearch to try to establish the birth (or at least baptism) date of my ancestor Thomas Merrick. Most of them point to a baptism at Weaverham If it's 1610 then I have his father as John Merrick (said to be 1589-1627) although again this is unsourced, so I guess it would be at that point that my research runs out anyway.
I don't know what you've been looking at on familysearch, but they have a wealth of records pertinent to this, and I don't think your research will 'run out' just yet!
There would seem to be what look like several brothers having children baptised at Weaverham in the early 1600s. John, Richard and Edward. I looked at a couple, but they didn't give any place of residence (they may not have lived exactly in Weaverham of course). It would be a good idea to look at the actual images for all of them just in case. You are very lucky that these events are directly linked to the images in the Weaverham registers - and it's all free! It doesn't happen very often that a) you can view the registers at home, and b) each event is directly linked to the actual page in the register.
Unfortunately Thomas's baptism in 1610 doesn't give his father's name.
However, the one on 14th March 1607, which is transcribed as "Kino", gives the father as John. If you look at the image, I'd say that first name is an abbreviation is "Ricd" - for Richard, and it gives father John's place of residence as Cuddington, Just a couple of miles away from Weaverham.
4th May 1613,"Ales" (Alice) Merricke wife of John was buried at Weaverham.
27th Sept 1627 John ("Johes" but indexed as "Johea" on fs), Merricke of "Bag Lane" was buried at Weaverham.
And there is a will for John Merricke of Cuddington written Sept 1627, I can't see the date of probate, but fs have it as 1628.
It is an absolute treasure chest of information.
John only has 2 children, Thomas and Margaret. So Thomas gets the lion's share.
I won't spoil the fun, but it gives not only John's father's name, but also the names of both his grandfathers! and his brothers are named as Edward and Richard as was thought initially.
So a gold mine of information.
It looks as though his daughter Margaret was an illegitimate child of his baptised Dec 1617. Mother Margaret Stringer.
You could also look for wills of John's brothers, and HIS father and grandfathers of course. findmypast has Cheshire wills.
Added: surely all these records would have been on findmypast too? - did you look there?