I think he cried because for the first time he saw himself as the sheriff and not one of the outlaws, realizing he had abandoned his fetish
Before talking about that, let's talk about my opinion of what made him not wanting to hurt Sono anymore. Usually when Koto fantasize hurting Sono, he knew it wasn't real. Then feeling firsthand the fear of him really dead override the arousal his fantasy brought. After that everytime he thought of hurting him, he could only remember the fear he felt back then. And when he watched the movie at the end, he saw the hero as Sono, while before in his fantasy he often likened Sono to the hero. That means Sono override the image of the hero within himself. And when the hero was dead, he saw it as Sono being dead. Hence why he cried. That's my own interpretation of the story though. It's possible that the author might've actually had different intention from my interpretation, who knows.
In the end he cried because he didn't remember about how he wanted to kill the sheriff in the movie like he wanted to in the beginning right??