Ron and the Horcrux: An Alternate Reading
I've read a whole bunch of theories and discussions about why Ron was the most affected by the Horcrux, and I just want to throw my two cents in.
One of the more popular theories seem to be that either the Horcrux was purposely singling him out because it sensed that Ron would destroy it, and another seemed to be that he was carrying much heavier insecurities and burdens than both Harry and Hermione. (This is as I have seen only though.)
While Ron did have quite a lot of worries and insecurities, they weren't significantly more than Harry's or Hermione's. Harry had the weight of leadership and the prophecy on his shoulders. Hermione has been entrusted with not only researching the Horcruxes, she was also practically carrying the logistics of their operations at that point. Any failure or mistake on her part could hold dire consequences for the Wizarding World. Ron's fear for his family and his insecurities regarding his relationships with the people he loves isn't more or less of material for the Horcrux, it's simply a different flavor of the same suffering.
No, I think that Ron was simply more VISIBLE in the way he reacted to the pain. And this happened or two reasons. First, Ron is the member of the trio who is most comfortable expressing his emotions. Second, (and more importantly), he was also the only person in the Hunt for whom leaving was actually a legitimate option.
First: Expressing Emotions.
Harry is the type to endure pain in silence. He is used to hurting, and even more used to no one being there when he needed them the most. He learned to not bother asking for help long before Hogwarts, and his time in school did not make that mentally better. He was constantly disbelieved, and he had to finish adventures alone more often than not. Harry is used to just riding out the pain, and that makes emotional outbursts rare for him. This indicates a tendency towards internalization and self-isolation.
In the Hunt, this translates to getting buried under the weight of leadership. It means feeling as if he has to take everything on his own. Even more importantly, it means sitting in that cesspool of toxic emotion until he suffocated. Worst comes to worst, Harry blows up, but until then, it looks like Harry brooding in silence.
Hermione, on the other hand, functions by compartmentalization. She is highly logical, and part of that means that she works best when there is structure. Sometimes that structure is external. Most times though she builds it herself (as we see through her rigid study schedules), and this holds true for her emotions.
She is a highly emotional person, but she also very rarely acts on them. Her slapping Malfoy, setting the canaries on Ron, and attacking him after his return are so shocking both to the readers and her own friends because her emotions are often quite contained. Instead of acting on them in the moment, she channels her feelings through working and solving the problems that elicited the emotions in the first place. And this is only if she decides not to take the high road.
In the Horcrux Hunt, this looks like her constant movement. She keeps planning, brainstorming, managing the food, and ordering both Harry and Ron around. She had a to-do list, and it is through this constant movement and work that she alleviates the possible negative emotions that the Horcrux may have stirred up within her. Aside from the occassional snappishness, the negative effects on her did not result in visible outbursts.
Now to Ron. Ron is a very emotionally expressive guy. Furthermore, he's a loud guy. Coming from a huge family with a lot of competition, being loud is the only way he gets heard. And we see this all throughout the books. He is outspoken with his opinions. If he finds something stupid, he says so. If he is happy, he shows it. If he is nervous, it affects EVERYTHING he does (see: being the Quidditch keeper). Relative to Harry and Hermione, Ron is very much in touch with his emotions, and that makes him very reactive.
And this means, that coupled with the fact that his sore points all have to do with his place in the team, the effect of the Horcrux means loud blow-ups at the people he perceives have slighted him. The targets for his insecurities are RIGHT THERE, and his already short fuse has been made shorter by not only the Horcrux but also the terrible conditions of the Hunt. Ron loses all control of his emotions, and it manifests as anger against the people he strongly feels have not valued him.
Second: The Option of Home
By the time the Horcrux Hunt started, Harry and Hermione don't actually have homes to come back to. Even worse, there is no chance of asylum for either of them. Harry Potter was condemned by a prophecy and is Undesirable#1. The closest he has to a family is the Weasleys, and his presence will place them all in unnecessary danger.
Then not only is Hermione a muggle-born, but she had voluntary removed herself from her parents lives, and she did it in a way that is pretty difficult to return from. Unlike Ron who is believed to still be with his parents, Hermione is very clearly with Harry. Even if she wasn't an Undesirable, she would still have been hunted by virtue of being muggle-born. There really is no place where she could go back to and expect to remain safe.
Ron, on the other hand, while considered a blood-traitor, is STILL pure-blood. In fact, him going home is probably what is safest for his family. It is an option that he and only he ALONE has. Him storming out of the Hunt isn't a sign that he was more affected than most - that happened because HE COULD. He has a family to come back home to, and one with resources to not only support him, but actually keep him safe. Yes, they'd be mad at him, but they also wouldn't turn him away.
Of the three of them, Ron was the only for whom leaving actually made sense.
While Ron wasn't disproportionately affected by the Horcrux, he did react in the most VISIBLE manner. This led his suffering to be the most visible among the Trio's, but this does not mean that his suffering was necessarily "worse" by any significant degree. Nor does it mean that he was specifically targeted by the Horcrux. Ron blew up because he could. He left because he could. He was angry and he felt that it was the right thing to do.
His arc is about overcoming his insecurities and learning to stay. To attribute his leaving as anything other than his own personal decision is to do a disservice to his character and development.