Don't know if this is useful, but my research strictly on ancestry.com has turned up the following children of Johann Georg Weyrich:
Johann Nicholas Weyrich 1723 – 1792
Maria Barbara Weyrich 1726 – 1767
Anna Katharina Weyrich 1728 – 1731
Johann Wilhelm Weyrich 1731 – 1795
Johan Christian Weyrich 1733 – 1771
Anna Margaretha Weyrich 1735 – 1770
Mary Elizabeth Weyrich 1738 –
George Weyrich 1740 – 1765
Peter Weyrich 1749 – 1823
Valentine weyrich 1750 – 1819
Note that there are three "John" Weyrich's, all substantially older than Peter. However, in searching the ancestry.com records for the three John Weyrich's, I can find no mention of a David Weyrich. In one family tree, the Challis family tree, I found mention of a David as the son of Peter Weyrich, but that David was said to be born in 1801 in their record, and they have no substantiation for that.
BTW, again per ancestry.com, Johann Georg Weyrich's father was Hans Niklaus Weyrich, 1620-1685, born and died in Germany.