Please contact theWeiser Family Association, 55 Kohler School Road, New Oxford, PA 17350. They have the complete record of all the decendents of John Conrad Weiser. This information is backed up by paperwork that is accepted by geneaologists. There are many other Weisers in the US who are NOT related to John Conrad Weiser. The records the Weiser Family Association have available will likely reduce the amount of time spent on research.
I would guess (I don't own the Weiser Families in America set) but based on the date of George Weiser's birth he may be brother to John Conrad Weiser, Jr. born November 2, 1696. Conrad was in New York(briefly), Lancaster, Reading, Berks County, Philadelphia and Wolmelsdorf. I will check my book "Conrad Weiser Friend to Colonist and Mohawk" to see if he was in Beaver County at any time. This book is a compilation of his diaries, and post again this evening.