Itte.

Both the Milgram series and Itte are some of my favorite 3-4 minute music videos ever. They explore extremely heavy themes in some of the most heartbreaking ways with some of the most emotional singing and lyrics I've heard. I don't want to spoil the themes, but they're extremely short so please give them a shot!  

If it wasn't for a post I found, this rec wouldn't have come to be, but it has opened my eyes that Yoru Ni Kakeru and Itte focus on suicide and lovers. You have to do your homework with these two MVs, but once that is done and over with, you are overwhelmed with dark stories/messages with a catchy song on top of it. It's a sad thing, but one that is also quite heartful as opposed to just existing for the sake of it. 

Suicide brings sadness, it's not a fate people or people related to an individual would love to be in. That is entirely true for MVs Say It. and Ruru's Suicide Show. The stories based on both cases, also come along with a high-quality MV that conveys the tone and atmosphere of these MV exceptionally.