I have been trying to find something on your family for you but need more info if you have it.
When were children Willliam and Margaret born and where?
Where were William James Ness and Sarah Easton Brown married? Scotland or U.S.
Was Sarah from Scotland? Do you know when and where she was born?
Linlithgow and Broxburn are both in West Lothian so I looked for any NESS families in that area.
In 1901 census for UPHALL, WEST LOTHIAN there is a family - parents William age 46 and Margaret NESS age 41, with children Annie G. age 14, John age 13, Thomas age 12, William age 9, James age 7, Janet age 3
This is the only NESS family in the West Lothian area.
It may seem unlikely as there is a son William and a son James and yours is William James, but believe me it is not totally out of the question. For some reason we gave our youngest son the same first name as his older brother's middle name - guess we liked it a lot - I cannot remember why we did that , but we did. I guess it seemed like a good idea at the time but they laugh at us for doing it.
There are lots of NESS' in East Lothian where my NESS ancestors are from, as well as NES families in other spots. So it is hard to know if the above family is the right one or not. Do you know the names of any of your William James siblings? That may help.
If you can post all of the info you have on this family I will do some more looking for you.