What sympathy does the writer convey for Walter in this play and why?

Hansberry feels sympathy for her character, Walter, for a number of reasons.  An African-American herself, she personally watched men struggle with issues of racism that kept them working in subserviant jobs.  Also, Hansberry was raised by parents who were very progressive and politically active.   Engendering a proud racial identity was something Hansberry frequently championed  in her work. 

As for the her character, Walter longs for the respect and opportunities that white Americans enjoy for himself, his son, and his wife.  In Act 2.2, he dreams aloud,  saying:  "You wouldn’t understand yet, son, but your daddy’s gonna make a transaction . . . a business transaction that’s going to change our lives. . . . That’s how come one day when you ‘bout seventeen years old I’ll come home . . . I’ll pull the car up on the driveway . . . just a plain black Chrysler, I think, with white walls—no—black tires . . . the gardener will be clipping away at the hedges and he’ll say, “Good evening, Mr. Younger.” And I’ll say, “Hello, Jefferson, how are you this evening?” And I’ll go inside and Ruth will come downstairs and meet me at the door and we’ll kiss each other and she’ll take my arm and we’ll go up to your room to see you sitting on the floor with the catalogues of all the great schools in America around you. . . . All the great schools in the world!"