Pope Urban's support of Galileo existed more on a personal one than a public one. The Pope was not directly behind Galileo's heresy trial however he did not make any move to override the decision made by the Holy Office of the Inquisition. Pope Paul, who approved the Edict of 1616 could have also pardoned Galileo but he did not. The trial was arranged and held by the Holy Office of the Inquisition, not Pope Urban and not the Catholic Church.
Pope Urban was only one of Galileo's many influential friends. One must remember that Galileo was associated with the Medicis as well as several people in royal and top political positions, e.g., Ambassador Francesco Niccolini and Francesco Cardinal Barberini.
When Galileo was allowed to return to Arcetri on the condition he would remove certain passages from the Dialogue. However, Galileo was basically under house arrest in Arcetri and still treated as a heretic by the Holy Office of the Inquisition which would mean that he could not be buried in a manner fitting to his position.
By this time, however, Galileo was getting old, was frequently sick, and was exhausted. He simply wanted to go home. Going home to Arcetri also meant being within walking distance of Convent of San Matteo where his eldest daughter, Maria Celeste, lived.