Duke is trying to destabilize the empire, right? I believe he is the ruler of a dukedom on the border of the empire and heinley's kingdom? If the empress and emperor get divorced and an incompetent one is put in her place, his country will gain more power. I think playing cupid for Heinley is just a secondary motive that happens to align with his own goals, hence why he seems so shady and feels so guilty. He doesn't actually wish the best for his friend and the empress, he's using them.