Mr. Robert (this is his first name) is the maternal grandmother's "friend." Since he is living with her, he is more than a friend, but as old as Grandma Sands and Mr. Robert are, they are probably just two close companions who keep loneliness away.
Nevertheless, out of loyalty to her dead father, Momma is not very comfortable with Grandma's relationship with this man. She says to Grandma,
"I just don’t understand what’s going on here. How come I never knew him? Did Daddy know him?”
....Grandma Sands looked at her for a minute. "'Lona, things are different from what they were when you left. Nearly everything changes. Your daddy’s been gone for almost twenty years." (Ch. 12)
Kenny narrates that his grandmother no longer smiles when she explains that Mr. Roberts is her "dearest friend." Probably Grandma cooks for Mr. Roberts and he does yard work and cuts fire wood for them. They love each other in a platonic relationship, and would be very unhappy without each other because then they would each suffer a terrible sense of isolation. Together they can enjoy the remaining years of their lives. And, as Mr. Roberts explains about his old coon dog and himself--"We just stopped...lost the desire"--he just wants the comforts of a warm bed and a good companion with Grandma Sands.
It is entirely possible, too, that Mr. Robert knew Grandma Sands in a different way years and years ago. But she chose Mr. Sands and so Mr. Robert was left out. Possibly after Mr. Sands died and Mrs. Sands reached out to him, Mr. Robert chose to live with her in order to not be so lonely.