Popeyesays said:
To hasted the death along it was customary to break the legs of the victim after a few hours on the cross. ...What is unusual is that He was taken down promptly.
The hastening of death and the removal of bodies so quicky had to do with the coming passover as did the speedy trial of Christ by the Jews. There could be no putting to death during the passover neither could there be the handling of dead bodies according to Jewish law (they would be unclean and unable to participate in the rite).
While the Romans were not bound by Jewish law, appeasing them was one of the primary funcions of the governor of Judea (the fewer problems the better for the Roman Ruler as the Jews were an unruly bunch).
While Pilate probably had no regard for an individual life or the sufferings thereof, he more than likely had a sense of justice under Roman law that would not want to see an injustice done. This was most likely the reason for any compassion shown to Christ (as well as the dreams of his wife, Matt. 27:19).
Pilate had to balance this sense of justice against unrest in Judea (the mob of Jews calling for crucifiction was getting out of hand, spurred on by the pharases). His position as governer depended on keeping his territory civil.