The first thing I found was a Mary Wright that seemingly would have fit perfectly:
John Wright, Esq., of Kelvedon, who m. 1714, Elizabeth, dau. of Robert Brooke, Esq. of Weston Underwood, co. Buckingham, who d. s. p. 19 June, 1718. He m. 2ndly, 1733, Constantia, dau. of Francis Carington, otherwise Smith, Esq. of Wooton Hall, Warwickshire, and
Aston Hall, Shropshire, and great-granddau. of Francis Carington, Esq., brother of Charles 1st Viscount Carington, and had issue, John, his heir, b. 1740; and two daus.,
Mary, b. 1735, d. 1753; and Constantia, b. 1736, a nun.
https://books.google.com/books?id=H65CAAAAYAAJ&pg=PA1553&lpg=PA1553&dq=James+Mary+Wright+Anston+Hall&source=bl&ots=ABezQDzmVk&sig=y7ZejcrsJ7AJ17RyHPQE8SRCcaM&hl=no&sa=X&ved=0ahUKEwjX8bORzaTTAhUL4IMKHc8zDRsQ6AEIQjAF#v=onepage&q=James%20Mary%20Wright%20Anston%20Hall&f=falseBut as we see, this Mary dies in 1753. Still, it might be worth the trouble to check to see if you can find that burial record for yourself, and that she did not marry somebody inappropriate or went to live with someone without being married instead. It all might be just a coincidence too and that these people have no connection to your family whatsoever. *shrugs*
Some Mary Wright-White marriages:
Mary Right who married Henry Waite on the 16th of May 1731 at Billinghay in Lincolnshire, England
Mary Wright who marries John White in 1733 in Tetbury, Gloucestershire, England
Mary Wright, spinster, who marries Edward White, a bachelor of Whitehead in Warwick, on the 12th of March 1749 at Southam (or Wormleighton ?) in Warwickshire, England
Mary Wright who married Leonard Whaite on the 4th of February 1750 in Lancashire, England