I think you're right. Francis Fenton & Ann Bery married Jan 1 1716/17
Formal Citation that should be used: "Marriages by Rev. William Allen of Greenland, N.H. New England Historical and Genealogical Register 65:352. (1911) [https://archive.org/details/newenglandhisto62unkngoog/page/n400 Link]
I am puzzled by the marriage in New Hampshire, what was he doing there I wonder.
The Profile for Ann is open and adoptable. You can adopt her and change the Last Name at birth field to Bery. I feel quite certain she was not born in Willington, which didn't exist then. Considering the marriage, that would be the place I would hunt for her parents.
Pre-1700 general advice.: In general, feel free to update pre-1700 profiles that need proper sourcing and more information. First, read what’s already on the page. Ask yourself: Does what I'm adding add value to the profile? Always, always source your updates/changes/facts/statements, preferably with primary sources, and using inline citations. Before you make major changes (changes in relationships, or vital statistics) make sure you attempt to contact the profile managers and/or the Project. It's always polite to contact managers if you're going to do a major overhaul.
<!--
/* Font Definitions */
@font-face
{font-family:Cambria;
panose-1:2 4 5 3 5 4 6 3 2 4;
mso-font-charset:0;
mso-generic-font-family:auto;
mso-font-pitch:variable;
mso-font-signature:3 0 0 0 1 0;}
/* Style Definitions */
p.MsoNormal, li.MsoNormal, div.MsoNormal
{mso-style-parent:"";
margin-top:0in;
margin-right:0in;
margin-bottom:10.0pt;
margin-left:0in;
mso-pagination:widow-orphan;
font-size:12.0pt;
font-family:"Times New Roman";
mso-ascii-font-family:Cambria;
mso-ascii-theme-font:minor-latin;
mso-fareast-font-family:Cambria;
mso-fareast-theme-font:minor-latin;
mso-hansi-font-family:Cambria;
mso-hansi-theme-font:minor-latin;
mso-bidi-font-family:"Times New Roman";
mso-bidi-theme-font:minor-bidi;}
@page Section1
{size:8.5in 11.0in;
margin:1.0in 1.25in 1.0in 1.25in;
mso-header-margin:.5in;
mso-footer-margin:.5in;
mso-paper-source:0;}
div.Section1
{page:Section1;}
-->
