My theory is that Crybaby died after the events of Sippy Cup, being poisoned by Mommy.

(I know Mel confirmed that Crybaby had just passed out, but the evidence lines up too well)

Before Sippy Cup, she didn't display any powers but in every Crybaby song after (Except for Mrs Potato Head and Training Wheels), she displays a new type of power:

Carousel: Levitation (Chasing after Alphabet Boy)

Alphabet Boy: Changing size (Getting taller to sit on top of the fridge)

Soap: Physical manipulation, telekinesis, and electricity manipulation (Breathing bubbles, opening the door and flickering the TV)

Pity Party: Telekinesis (With the party hats)

Tag You're It: Telepathy (With the cashier)

Milk And Cookies: Physical manipulation (Taking her head off and putting it in the cookie jar)

Pacify Her: Physical manipulation and telekinesis (taking her head off and putting a pacifier on Basic Bitch)

Mad Hatter: Physical manipulation, levitation, changing colours of objects, and changing size (Levitating to the roses, changing them red, peeling her skin off her face, and shrinking to fall into the bathtub)

Also note the fact that Crybaby is dressed as an ANGEL in the Sippy Cup music video and sitting in a white void.

There is one contradiction, being that she looks the same, but my thought is that she wasn't being guided by Lilith yet, so she didn't have anyone to change her. (I know that one's a bit a stretch.)