I think I can help you. I'm descended from John Beans brother of William Randolph Beans. My siblings and I have uncovered several more children of Aaron Beans. Sisters Rachael, Sarah (in whose home Aaron lived until his death), and Lucinda. Brothers Timothy, Ration (mentioned in Aaron's obituary)and three children deceased (mentioned in diary records of a Reverend from Portage county). Mary Walter Beans'father was John Walter and his wife's name was also Mary. We have a copy of a will that was probated for John Walter and which names his daughter Mary w/ her husband Aaron Beans. At the time of the will Mary had two brothers, Henry and John, and sisters Sarah (John B.) Roller, Lydia (Benjamin) Lodge, Susannah ( John) McKee, and Molly Walter.
We have not been able to find written evidence at to the parentage of Aaron Beans but all signs point to only one gentleman, a Timothy Beans, and his wife Mary Randall Beans as the possible parents of Aaron. Timothy is the son of William and Hannah Balderson Beans of Loudon County VA.