Katherine Johnson is a married woman with wealth and high social status. Her friendship with Tesla is a sign that Tesla has arrived at a new level of the social strata. Though Tesla gets into the New York 400 of most important people, he still feels small.
Katherine was most likely representing herself and her husband to the inventor. Katherine often cared for Tesla as if he were her child or spouse, bringing him meals and offering other ways of nurturing and caring for Tesla, in order to help Tesla stay focused on his projects.