Sue, I still keep a sub to American Ancestors. Searching Webster in Rockingham, NH, I found a wealth of hits:
Census, Tax and Voter Lists (8233)
Vital Records (incl. Bible, Cemetery, Church and SSDI) (4910)
Military Records (468)
Genealogies, Biographies, Heraldry, and Local Histories (31)
Journals and Periodicals (23)
Court, Land and Probate Records (2)
I think Rockingham is in fact a county of the state of New Hampshire. I could not find any city, town or village by the name of Rockingham there.
Perhaps most useful for you right now, I see there are genealogies online such as these.
JOHN WEBSTER. The Fifth Colonial Governor of Connecticut
"John Webster and his wife Agnes came to this country from Warwickshire, England, in the Spring of the year 1635, and settled at Cambridge, Mass." 32 pages.
The New England historical and genealogical register
by Waters, Henry F. (Henry Fritz-Gilbert).
See pages 159-160 in this volume, but there are many others. Volumes 1-77 cover 1847-1923. This section on "The Webster Family" is just one hit I got.
There are probably plenty more, and I would expect most or all to be available free online at archive.org. You could have a poke around.
I would love to stay and poke with you, but I have got to get ready and go out to a medical appointment. Good luck!