Question about Sayori's behavior (an analyse question about her) and the poem Hole In The Wall...

Can someone explain to me her character? I finished the game, but I do not get something:

Sayori is really cheerful. And she cares about other's happiness. But if she have depression because she gives all of her dreams to other people, and she tries so hard to make them happy that she feels her own happiness is not present anymore, then why she keeps on caring about the MC so much and tries so hard to make people happy around her?? Is there a reason for that? for that obsessive behavior that she tries to make everyone so happy? I get that she thinks she isn't worth the effort to be care about, but still what is her motive to make people so happy, what she gains from it, is a mystery to me...

Also about that poem did someone get it? I'm trying to get it myself but...Well I just can't i guess haha

Thanks for helpers.