This is the correct family. The father John Catesby Weedon (1797-1887) married Elizabeth Trone. Both are buried in the Trone-Weedon Cemetery, Manassas, VA, along with their son Sgt. Peter Trone Weedon (1835-90). Family sources mention the brother John kia Chickamauga. John C's father Augustus Weedon (1751-1833) was a Revolutionary War veteran.
I've not been able to find a Mobile or 1860 census connection. A copy of the 1861 Mobile directory is at Duke U., and maybe that could give the occupation. The CSR's do not.