I am using both James N., Arnold's "Vital Record of Rhode Island" and Craig Rice's online data to match this marriage entry in Arnold's "Vital Record of RI" with this particular Nicholas. They were married by Sylvester Sweet, Justice.
Arnold's transcriptions of East Greenwich marriages shows a Nicholas Whitford marrying Ruth Shippee, 29 Sept 1764. Is this the one? Probably. He likely married second to Elizabeth Potter. Compare their wills. It is unclear whether they each had a daughter Elizabeth, or whether there was only one. His will mentions his wife Elizabeth; sons Ezekiel, Nicholas, & John; and daughters Eleanor Rice, Hannah blanchard, Mary Weaver, Ruth Harrington, Elizabeth Whitford, Sally Greene, & Olive Whitford.