It's really difficult to draw any particular sympathy for Stanley. He is intensely base in terms of how he approaches reality. For Stanley, consciousness is defined by his ability to take what he wants and to assert his power in a form of emotional and physical control. In this, Stanley is really difficult to find sympathetic. If one were to take a larger psychological point of view, perhaps there is something in Stanley's background that made him the way he is today. This would be something that could bring out sympathy in that something in Stanley's background helped to create him in the way he is presented. However, I am not sure that this is Williams' intent in his characterization:
In earlier versions of the play, Stanley had a gentler, ineffectual side, but in the final writing of Streetcar Williams made him Blanche's complete opposite—angry, animalistic, and reliant on his basest instincts.
In the end, this is where it becomes a challenge to find sympathy in Stanley.