At least part of it's that we have our _own_ emotions, that we don't mirror others' emotions very easily, maybe especially with something like your sad movie, where our cues for what the actors are feeling are limited to sight (of their faces, and it's not much of our whole field of vision) and sound (their voices, and maybe sad music background). (Also depends on just how good at acting the actors are!) That leaves us smell, touch, and taste that aren't affected at all. In the Real World, with other people, we don't even get as many cues or do as much mirroring as NTs do -- someone was talking about mirror cells in our brains that, when someone smiles at us, we tend to smile back at them, and the very feel of the smile on our own faces makes us feel happier. It was said in whatever (maybe here, maybe some of the reading I was doing, I don't remember), that Aspies don't have as many of those mirror cells, or connections, as NTs do.
I know movies, television, don't affect me very strongly, except one kind, the scary horror movies, and the gross shots of autopsies and dead bodies in pieces, etc, that shows like CSI seem to specialize in. Those affect me much too strongly, may give me nightmares. I've learned to be careful what I watch. There's one image I saw on television about ten years ago that has stuck with me and still pops up at unwary moments.