How much control does Zeus have over what happens in the Iliad?

Zeus only has as much control as fate allows him. One of the saddest parts, I think, is when Zeus wants to save his son Sarpedon, who is fated to die. He could do it, but Hera tells him, "Do what you will, but none of the deathless gods will ever praise you for it." Of course, it's easy for her to say since it isn't her son, but she's right. All he can really do is keep events on the course they are supposed to take, and grieve.