In the current Arch-Emperor Dynasty, the Arch-Emperor was actually only a figurehead. The Grand Heavenmaster held the true power, and controlled both the Son of Heaven and the aristocracy. However, that was mostly what happened behind the scenes.
Furthermore, in the grand scheme of things, it didn't matter too much that the Arch-Emperor was weak; he was only the current reigning Arch-Emperor. Nobody could say for sure what would happen when the next Arch-Emperor rose up. Furthermore, the Grand Heavenmaster had not followed the example of the Celestial from Heavenspan Island, and turned himself into an emperor. As far as many people were concerned, the Grand Heavenmaster was actually being quite benevolent and merciful.