I didn't really cry but I got very emotional with BTS - Spring Day & B.A.P - 1004 Angel (the scene with Himchan in front of the mirror I just couldn't help it)
Yh I'm really soft
Butterfly - Loona
And for reasons I cried listening to all of Cle 1: Miroh for the first time so I kinda watched Miroh like it was filmed from my trashy Windows phone
No videos that I can think of, but certainly some songs do it. Of particular note is (G)I-DLE's Say No/Put it Straight, which had me welling up on first listen, before I knew what any of the lyrics meant...