Katherine's parents were Alexander Balcombe and Rebecca Carr. I have no birth dates for either parent, but I do have a death date for Alexander, 4 May 1711, Providence Rhode Island. Rebecca Predeceased him for Alexander remarried and had several more children.
Katherine (1673-1729) was married twice that I'm aware of, the first time to Isaac Allen, who died in 1692. Katherine later married Daniel Jenckes, who was born in 1663 in Pawtucket Rhode Island, he died in 1698. To my knowledge there were no children of either marriage.