To finish telling Molly's story, I decided to discover more about Molly and her family. Vital records are spotty for this time period. I did check the Barbour Collection (which covers vital records up to 1870) but discovered no mention of Mary Graves in East Haddam... so it was on to the back-up sources! The East Haddam Congregational Church kept records of the community's baptisms.
While the original church records are stored in the state library, the New England Historic Genealogical Society has a transcription that they've made available online. You'll need to be a member to access the database. Once you've logged in, you can search the database catalog. I use the location search. Enter United States and then Connecticut. On page two, you'll find "East Haddam, CT: Records of the First Congregational Church, 1704–1802."
This transcript has a bit of a search issue -the writer used possessives in their records. Be sure to consider adding an extra s when searching last names. If you fail to do so, you may be informed that a record doesn't exist. I tried both ways and found my ancestors as "Gravess."
My search wasn't as fruitful as I would have liked. I located a baptismal record Benjamin, Molly's father, in 1734. Despite searching from 1763 (Molly's birth) to 1780 (the date of Benjamin's death), I didn't find one for Molly. Why? It's possible that the family may simply have lived closer to another church. To be thorough, I should also check the records for churches in Lyme and Colchester. That's a project for another day!