Liz, such interpersonal stress usually does not cause physical illness as such, but it can certainly cause physical symptoms which are exactly like those caused by physical illnesses. As others say, chronic stress can alter one's immune system and in other ways contribute to the development of physical illnesses, though that usually takes some time to develop. Anyhow, why should we only bother about physical illnesses --- feeling miserable is enough to deserve understanding and help.
As Zena says, talk to your stepfather about how he's affecting her, and enlist the mother in convincing him to lighten up. And just as people can live up to your good expectations of them, they can also live down to your bad expectations, so even from his own point of view, his approach isn't even likely to solve the problems he thinks exist, but may be actively creating them.