How do you know for sure that the Sarah
Briggs who is a daughter of John in the vital records, is the same Sarah who stated that her father was William? Sarah is one of the most common names, and very possibly these are two different individuals. Another possibility is that the town clerk wrote the incorrect father's name in the vital records. Perhaps
Elder Wightman wrote down the wrong name. Without personally seeing these documents, I can't offer any other explanations. However, the will of John
Briggs of East
Greenwich, written 26 Aug 1795, does mention a daughter Sarah, single at that time. So, if your Sarah was married in 1778, she must be a different person -- inless she divorced and resumed her maiden name.