There is a simple way of looking at Ralph's outburst, one that perhaps the naval officer would have, that suggests that he is crying because they have finally been rescued and he is relieved at the prospect of going home. Certainly one could assume that Ralph would be overjoyed at the prospect of having rules and civilized society about him again given how hard he tried to make it work on the island.
But as Golding points out with his description of why Ralph is weeping, it has very little to do with the rescue. He now understands the depths to which humankind can sink because of what he has seen on the island. He also knows that he is guilty (in part) of Simon's murder, that he too is capable of the most atrocious violence.
And it is perhaps this realization that most deeply wounds him as he is weeping for the fact that this darkness, "mankind's essential illness," cannot be cured. He knows that it is a part of all of them.