Mrs. Jones wants Roger to know they have something in common in order to teach him "right from wrong."
When she initally grabs Roger, Mrs. Jones asks him if he is going to run away if she lets him go. When he responds that he will, Mrs. Jones's intent becomes clear: "You ought to be my son. I would teach you right from wrong." From this point, it becomes clear that Mrs. Jones seeks to instruct Roger. She knows that Roger is lacking in guidance and assumes this leadership role, if only for a moment.
It is clear that Mrs. Jones understands the reality that Roger faces. Letting him know that they share common backgrounds is how she communicates this to him. She operates as the voice of experience for Roger when she says, "I were young once and I wanted things I could not get.” In emphasizing the struggle she has faced in her life, Mrs. Jones wants Roger to recognize that there can be a way out for him: "I have done things, too, which I would not tell you, son—neither tell God, if he didn’t already know." Like her, Roger can make active choices to embrace dignity and honor in his life. He does not have to embrace criminal activity. Mrs. Jones lets Roger know that they share similar paths so that he can be more than what he currently is. Creating a bond of a shared past is the only way she is going to be able to instruct him in this lesson.