None of the data on the profile is sourced (without knowing what 'Rosalie's family history binder "White's".' contains), so it's not clear whether the following is relevant. ASSUMING birthplace Weymouth, Mass., is correct:
Massachusetts: Vital Records, 1621-1850 (Online Database: AmericanAncestors.org, New England Historic Genealogical Society, 2001-2016).
Weymouth - V1 p 338, Weymouth Births (transcribed)
Elisha, s. Samuell and Ann, June 16, 1702.