Well first of all, I'm not sure songs actually make me cry, unless I'm already really sad or depressed. Second of all, I tried to think metal songs that brought me to that sort of feeling and I can't think of any. Basically all singer songwriters and mostly women.
Swans- God Damn the Sun
This song is high art. This brings the whole world together in a tragic and meaningless disaster.
Rachael Yamagata- Horizon
It just has that feeling of "wow, I fucked up my life, but didn't realize until two years later."
Tori Amos- Playboy Mommy
Yeah, songs about moms have miscarriages are pretty sad.