Ugh! Grave of the Fireflies and Cinema Paradiso are both heartbreaking. And you've certainly tapped into something: Film is such a wonderful outlet for emotions.
There is, however, something to be said about watching these sorts of films with others and sharing in those nasty, illogical, vulgar, and messy things. Maybe it's just me, but the solidarity is a nice counterpoint to grief, sadness, isolation, and all those other fun emotions.