It's hard for me to sympathise with the emotional core of ASM2, as the argument of that movie seems to be that Peter Parker is a sociopath.
Gwen Stacey dies at the end.
1) If that scene had been handled well at least some people would have cried. I don't know of anybody who cried at that scene.
2) Peter Parker then mourns for some time and returns to being Spider Man.
The problem with #2 is that ... he returns to being Spider Man as he was before. It's the second time that Parker's error kill off a Stacey family member, but he goes back to being exactly as he was before. It's presented as some sort of triumph. As pointed out elsewhere, shouldn't the fact he killed a girlfriend that he wasn't supposed to date make him change and doubt himself and become a different spider man?
What's the emotional core of the film if his girlfriend dying causes no change in his identity?
I know a few who cried for #1. All non-comic book fans. Personally, I didn't cry because I saw it coming. But I did get sad when they were on the bridge and they finally figured out how to live together, because I knew what was coming next. I'd argue that to comic book fans, that was intended to be the emotional scene.
However, I'd argue the most emotional scene in the film is at the end with the kid. I almost broke down in theatres, to the point I was thinking to myself "This is ridiculous, I'm a grown man, shouldn't react like this". It really connected to my childhood and how I became a Spider-Man fan, and encompassed everything the character is about. One of my favorite endings ever, and I can honestly say I haven't felt so much emotion since the ending to TDK. It reminded me of everything I love about Spidey in the same way that ending reminded me of everything I love about Batman, granted TDK is still a better film overall.
As for the message, I don't think that's what the film is saying.
I don't think Peter is at fault for Gwen's death, at least not directly like with Uncle Ben and Captain Stacy. The thing is, Gwen made her own choice and chose to risk her life in order to do the right thing. She's grown with heroic figures throughout her life, particularly with her dad, and believes the way you live your life is more important than how long you live it. Which is a huge theme in the film and contrasts with Norman and Harry, who are more focused on how long they can live as opposed to how they live it. In Norman's case, he based his empire on prolonging his life and using illegal human experiments to do so, when he could have used that power more responsibly (sounds familiar

), but I digress. Point being, Gwen risked her life to be a hero and not just chose to, but believed that's the way to live life to the fullest. Peter tries keeping her out of harm's way multiple times throughout the story, which her father also did in the first film, but eventually has to come to grips with the fact it's what Gwen wants.
Yes, there will be casualties and dark moments throughout Peter's life - throughout anyone's life, really - but what separates heroes is how they pick themselves up and keep going for
others. We know that's what Gwen believed. "No matter what happens, I want you to promise me you will be who you are meant to be." In Peter's case, it's Spider-Man, and countless other people will continue to need Spider-Man, including that little kid.
Of course, this doesn't mean Peter is no longer mourning or won't try to be a better Spider-Man, but he must mask that sorrow with joy and laughter and continue to be Spider-Man for others. Essentially that's the ending's message, and it's a huge prevailing theme in the Spider-Man mythos. The idea that a down-on-luck kid can hide his pain with a mask and become something larger-than-life that other people should strive to be.
It's for the same reason why Spider-Man comics have the highest body count of supporting characters, but no one ever notices because his jokeyness and lighthearted optimistic spirit distracts you from it.