It happens to be a good bit too, but the film/show has to be trying to make some kind of emotional connection. In a really shallow action movie, I'll just be along for the ride and even if I kinda enjoy the film, I won't really care if someone dies. But if the film puts any focus at all on the emotional side of things, I'll start emphasizing to a ridiculous degree.
Some character deaths have left me upset for days. Even after watching the How I Met Your Mother finale (which I hated), I couldn't help feeling really bad for the mother. This fictional character who I hadn't even known for very long. It just felt like she had been used, and even though she wasn't a real person, that was hurtful to me.
I think this is part of why I tend to love coming of age films. They're specifically designed to help you empathize with the protagonist. I find it really easy to lose myself in these other characters.