That's pretty small for a grooved weight, Jay. Considering they range up to loaf of bread size and larger. Maybe it's a bola stone, another type of hunting weight? Not at all familiar with the nipple you mention as a feature. Looks like the groove took a detour! Cool find.
Regarding grooved weights from New England, our regional artifact guide describes them this way: "Artifacts in this class consist of small or large cobbles with a well-defined groove pecked longitudinally around the stone. Occasionally, a second groove encircles the stone, transversely at the center. This artifact...is thought to have been used for a line sinker. It may also have been used as a net sinker; some examples from New York had charred cordage intact."
On the other hand, Bola Stones:
the bola or boleadora, a summary of ethnographic artifacts from south america, clina and other cultures.
The natives in New England did use bolas, although there is no reason your grooved weight could not just as easily be a line weight. They do get classified with fishing gear in New England, but small ones could be bola stones too. Especially for snagging water fowl.