Hey fellow 41 year old dude, I also cry at this stuff. It seems especially pronounced when rewatching nostalgic productions with well written characters and conflict (I will not apologize for crying all the time during Avatar the last Airbender, as an adult man). No, I do not know what this means in regard to healthy emotional processing, it just is what it is. Mind you I also get unjustifiably angry or emotional in other contexts when I feel connected to the fate of a character and they experience injustice. So this might be a general marker for some level of empathy or maybe just emotional mimicry. Thanks for posting, I think this is something people should be okay talking about more.
Edit: I wanted to add this also occurs in other mediums, like video games. Cyberpunk 2077 was like a revolution in awareness for me, but largely because I experience DID to a degree in my life, and it really flipped the table of my understanding of myself seeing what I experience through the eyes of others.
Shoutout to this LIST! 100% certain I've been unable to contain my emotions watching all of these. To me that's a marker for quality, so props on your good taste!