Zeena's health problems serve her well in several ways. The first is that she uses it as a tool to manipulate attention and pity from those around her. She gets a lot of attention from various doctors, which is always a nice thing, and then her neighbors and members of her community pity her and give her attention also. They bring her food, talk to her, visit and find other ways to help her out. Zeena enjoys that attention; it's nice to feel loved and cared for, and people feel that most when they are ill and receiving attention.
Another way that Zeena's illness is beneficial to her is that it keeps Ethan working hard for them both, and from leaving her or pursuing his other dreams or hopes--which would also take him away from her. Through being ill, she is able to manipulate his emotions, constantly using guilt as a way to ensure fidelity, caring and attention. If Ethan starts acting out or being defiant in any way, all she has to do is claim feeling ill, and put a guilt trip on him about the expense for surgeries.
Being constantly sick also ensures that Zeena doesn't really have to do a lot of the work around the house. That is what prompts Mattie coming to live with them in the first place. Zeena can lie around and get better while Mattie does all of the hard work. That's kind-of nice, and Zeena gets away with it all in the name of good health.
All of this points to the fact that Zeena is probably more mentally ill than physically ill. She is attention-starved, manipulative, and self-centered. There are possible personality disorders that are manifest in those behaviors, and her neediness is definitely a drain on Ethan. I hope those thoughts helped; good luck!
By having health problems she is keeping Ethan with her. She keeps Mattie sends her away because she finds out that ethan is attracted to Mattie.Zeena can be considered ill in her personality.