It also affects taxes and the frequency of some events, such as the discovery and spread of technology. I haven't experimented extensively with the settings, but I've had success giving power to the burghers, since that gives me armies with no peasants (who'll break and run quickly, which scares the rest of my units), good tax rates and openness to new ideas. Another distribution that works well for me is 50% nobles, 50% burghers, for knights and about the best chance of teching up you can get.
Low loyalty can also cause rebellions. By the way, if you click on the rebel shield in a battle report, it will bring up the character sheet of the King of the Rebels. (What is he rebelling against?) In my game, he was Norwegian. You can conduct diplomacy with him, and even establish dynastic ties, which can give you another way to get back to his page. I once claimed his title and declared war on him, but, unfortunately, the game would not allow me to make a peace treaty. It might be possible to inherit his title, but I haven't done it and so couldn't tell you what effect that would have on the game.