From a quick analysis of where you're up to, I think there's a danger of jumping to conclusions and leaping across gaps without any evidence. You also seem not to have given us all the information you have. In more detail:
On Nov 2 Elizabeth Cryer married William Calverley at Rothwell nr Leeds.
I / we are looking for a breakthrough on Elizabeths family. We have nothing else at present.
Some investigation suggests that Cryer may not have been her birth name and that William above was not her first husband. So far the most likely possibility is as follows.
William Cryer married Elizabeth Gott on June 21 1586 at Kildwick, nr Leeds. A William Cryer died and was buried July 21 1598.
You refer to "some investigation", without going into details. If we knew what that was, we could either avoid going over ground you've already covered, or offer opinions on how much confidence could be placed on that investigation, or both.
Your subject line mentions Cryers of Grantham, but your message has nothing about Grantham.
Cryer is a surname found fairly commonly in the Keighley/Skipton area (as is Gott), but both are more widespread than that. I note that the Rothwell registers (in printed transcript form) have a number of Cryer entries in the first half of the 17th century, but apparently none earlier than the marriage of Elizabeth to William Calverley (in 1600 - you didn't give the year). So there were clearly other Cryers around as well as Elizabeth, and if you can trace their origins you might find something on Elizabeth too.
EDIT: See my next reply for a comment on the 1598 burial.Benjamin Gott 1762- did very well in Leeds during the industrial revolution and this sort of thing tends to drown out previous family history in internet searches so it may be the same family, but so far we have no way of confirming that
Can anyone help us here please?
Work backwards from Benjamin and see where you get to. But as Elizabeth is quite a common name, there's no guarantee that any that you stumble upon will be the right one.
As with any family, you need to be prepared to look beyond parish registers. Marriage licences and wills often provide evidence of relationships; if you're lucky you might also find a memorial that gives a bit more information than a simple burial entry.
Lastly, I wasn't very impressed by your criticism of this site. It has developed over many years to become a vast store of family history knowledge and advice - all available for nothing. It depends on the goodwill of its members, who, although they offer help freely, don't like to feel unappreciated. In that spirit, you might wish to revisit some of your own earlier queries, where you have not acknowledged the help you have been given. You can find them by clicking on your user name, then Show Posts on the left.