The people in the balcony--"the Colored balcony"--stand out of respect for Atticus Finch. For, he is possibly the first white lawyer in Maycomb County's history to take a black man's innocence seriously and develop a sound defense for the man.
Before the trial begins, as there is no room on the courtroom floor for Scout, Dill, and Jem to sit, they accompany the Reverend Sykes upstairs in the balcony section, normally designated for African-Americans. Four of them graciously relinquish their front row seats to the minister and the white children, who then have a great view of the proceedings. During the proceedings, Atticus utilizes all his skills to expose the fabrications of the Ewells and to make apparent that they perjure themselves with their false accusations against the kind-natured and charitable Tom Robinson. So persuasive is Atticus's cross-examination of Bob and Mayella Ewell that even Judge Taylor becomes convinced of Tom's innocence.
Furthermore, the audience in the balcony is impressed with Atticus's impassioned closing arguments and his appeal to the jury's Christian duty:
"I am confident that you gentlemen will review without passion the evidence you have heard, come to a decision, and restore this defendant to his family. In the name of God, do your duty."
Therefore, since, Atticus has demonstrated that he truly believes in justice for all regardless of color or creed, the African-Americans in attendance stand up in order to demonstrate their respect for him and his sincere efforts.