After his brothers had left him to complete their goal, Yazoo, one of the embodiments of Sephiroth, chose to stay with you instead. He didn't know why, but he felt nothing like the other two, and he grew sick of them. He was part of Sephiroth. He was Sephiroth. Literally the 70% of him as well. Kind of... Well, or so he thought. That was the point.
He felt... deattached from what he actually was. Like that blood in him died off. He wasn't supposed to have feelings like this. He knew this was a stupid decision, and it would probably get him killed, be it his brothers or their own death.
He was utterly infatuated with you, to say at the very least. Again, he shouldn't be, but he was. Nothing of this tied together.
"Please, forgive me... I want to stay with you." Yazoo muttered, kneeling down in front of you and lowering his head desperately. I've failed them. I've failed mother. They have no use of me, is what he wanted to tell you. However, he refrained. All he wanted right now was your forgiveness.