Why is this?
I guess that with sad songs, you're able to feel a deep emotional connection because of how subconsciously, everyone can relate to these feelings of regret. Nowadays, I realise that it's a common attribute of society's members to say they are "okay" when they actually aren't. This type of behaviour thus makes the song really sing out to you, resonating deep into your soul (excuse the corniness here)- like a hand reaching out, helping you break free of your constricted emotions just silently begging to overflow and be heard. It's like a silent scream or plea for help. Because you know ultimately, although there may be people who vehemently deny this, there is not one person in the world who never felt like they were trapped, and wanted to scream out to the world- not to anybody in particular, but just to say something, anything, even if nobody cares or listens.
What makes music so powerful is just how it is able to extract all these emotions from within us, even if we ourselves can no longer express those feelings in a physical form. Perhaps it's the reason why I usually enjoy standing in the rain when I'm really upset; because it's as if the sky is crying the tears which I can no longer cry.
When experiencing happiness, sure it can be felt on a really deep level, but I think what really leaves a much larger mental scar is the pain felt from regret, betrayal and loss. I think that's why it seems that although upbeat and bright songs are fun and can possibly lighten your overall mood, it doesn't emotionally resonate as deep with you as does a sad song.