The 1st Marquess of Rockingham, Thomas Watson-Wentworth, married Lady Mary Finch, 1701-1761, in 1716. This may be that Lady, her article in thepeerage includes this portrait and another, probably of Mary Finch-Hatton probably misidentified as Mary Finch. However, according to his Wikipedia article, the 2nd Marquess married Mary Bright and the Wikipedia article shows this portrait as being that of Mary Bright. The biographical portion of the keywords is limited because of this confusion.
From the-athenaeum.org/art. Also posted to the Reign of Louis XV - 1715 - 1774 Album here.