So I'm not sure I've got a solid answer to this (as in there isn't a film that I didn't really appreciate while young but have come to really connect with as I've aged).

But off the top of my head, the most obvious answer, strangely, is the LotR trilogy.

Not that I appreciate more now than I did then. I was a book fan before the films and have liked them since.

But as I've aged, I've come to appreciate more some of the core ideology that Tolkein put into the story in ways I probably didn't really notice that much when I was younger, at least not explicitly.

The way in which Sam is the actual hero of the story and Frodo actually fails ... the whole idea of putting the literal "little people" of the world (including Eowyn, a woman in a patriarchal story/world) front and center and turning them into the heroes, not because of their supernatural abilities (unlike cough comic book films cough), but because of their values and courage ... having corruption of "the hearts of men" being a major source of evil ... having people who are machine loving rather than nature loving being a major source of evil (Saruman and Sauron are the industrialists of Middle Earth) ...

Sometimes I think back on these things and the story and each time I'm just kinda struck by how much I'm like "fuck yea" for a 70 year old novel I first enjoyed as a 13 yr old.