I found a few info on Anthony's son James and Anthony and Bridget.
Anthony Burney in entry for James Burney and Amelia R. Little, "New Hampshire, Marriages, 1720-1920"
Name: James Burney
Birth Date:
Birthplace: Montreal, Ca
Age:
Spouse's Name: Amelia R. Little
Spouse's Birth Date: 1846
Spouse's Birthplace: Woodstock, Nh
Spouse's Age: 24
Event Date: 25 Apr 1870
Event Place: Woodstock, Nh
Father's Name: Anthony Burney
Mother's Name: Bridget
Spouse's Father's Name: Peter Russell
Spouse's Mother's Name: Pamelia
Race: White
Marital Status:
Previous Wife's Name:
Spouse's Race: White
Spouse's Marital Status:
Spouse's Previous Husband's Name: X
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Anthony Burney in entry for James Burney, "New Hampshire, Death Records, 1654-1947"
Name: James Burney
Titles and Terms:
Name Prefix:
Event Date (Original): 1 Mar 1935
Event Date: 01 Mar 1935
Event Place: North Woodstock, Grafton, New Hampshire
Gender: Male
Race (Original):
Race:
Age:
Birth Year (Estimated):
Birthplace:
Marital Status:
Spouse's Name:
Spouse's Titles and Terms (Original):
Spouse's Titles and Terms:
Father's Name: Anthony Burney
Father's Titles and Terms (Original):
Father's Titles and Terms:
Father's Birthplace:
Mother's Name: Bridgett Moffatt
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Marriage Certificate of Arthur Barney Point and Bridget Moffatt (Montreal, Quebec, Canada)
http://search.ancestry.ca/cgi-bin/sse.dll?rank=1&new=1&a...