The Mirror newspaper, Friday, 28 January 1916 Vol. IX, No. 35
Mrs. Edward GREGG of The Plains whose death resulted from pneumonia, and Mr. George SMALLWOOD of Halfway, who died with infirmities of age were interred in Sharon Cemetery last Tuesday.
I do not find a burial for George Smallwood listed in the Middleburg Cemeteries book, so the newspaper appears to be incorrect.
George W. Smallwood died nearly 50 years after his father. His father lived in Middleburg, which is partly in Fauquier Co, while George lived in The Plains also in Fauquier County. Burial at home would not necessarily indicate a family graveyard of his father.
You need to check Fauquier Co Deeds for any land owned by John or George. If George owned land, look for the sale of that land after his death to see if it mentions a graveyard on the property.