Brutus justifies the assassination by claiming that he killed Caesar for the good of the people of Rome. He also sates that he loved Caesar but he slew him because of his ambition for power.
Based on this excerpt, "feeling sick" contextually means to feel intense emotion that makes one feel unwell or nauseous. While the man is not going to actually become physically ill, he does experience emotional sickness. He would likely feel a deep pit in his stomach and would be chilled from the thought of the man losing his wife, yet still being kind to him.
