There were at least 2 main Eakin families in Delaware that I know of. One was a Samuel Eakin, there is alot of information on him in the historial archieves in Dover. There was also an Eliza McCay who married a Joseph Eakin, Eliza lived in Delaware.
I would make the suggestion that you contact the Presbyterian Historical Society in Philadelphia. I got a great deal of information on the Eakin's family there and they have an alpha file that might be helpful in looking for information on Ann.