Part of the answer to this fine question can be seen in this phrase on the last page: "the true, wise friend called Piggy." Ralph weeps for Piggy because a) he was wise and good, b) he was a friend, and c) because he was called Piggy. (He didn't get to go by his name.) There is both guilt and regret there for how things turned out with Piggy. Ralph feels responsible (and in truth, he is, in part). By contrast, Simon kept his name, and his visions led him to his fate in ways that Ralph didn't have nearly as much responsibility for.
I am not sure that the passage to which you are referring necessarily must be interpreted to mean that Ralph weeps more for Piggy than he does for Simon. Although the last line of the paragraph -
"Ralph wept for the end of innocence, the darkness of man's heart, and the fall through the air of the true, wise friend called Piggy" -
mentions Piggy by name and not Simon, it is the memory of Simon's death earlier in the same paragraph that causes Ralph to break down in the first place. The author describes Ralph's state of mind at the end of the story by saying,
"the island was scorched up like dead wood - Simon was dead - and Jack had...the tears began to flow and sobs shook him. He gave himself up to them now for the first time on the island; great shuddering spasms of grief that seemed to wrench his whole body".
I think it might well be argued that Ralph wept for both Simon and Piggy, both symbols of innocence and sacrifice whose lives were lost, victims of the baser nature of the human spirit (Chapter 12).
In the end, Ralph weeps for Piggy more than Simon because, Piggy was a true representation of innocence who had remained committed to belief in order and civilization.
"Ralph wept for the end of innocence, the darkness of man's heart, and the fall through the air of a true, wise friend called Piggy." (Golding)
When the Naval officer asks who is in charge, Ralph says he is, he sees Jack, who remains silent, he still has Piggy's broken glasses on his belt.
"Ralph is unable again to express the truth behind his actions. He accepts responsibility for the island and weeps for the loss of innocence."