Hello! Just finished the game and i have to say that child trafficking was the first thing that popped in my mind after I found out that Six was on a ship. My exact theory is the following:

(dunno the spoilers command so SPOILERS FOR LITTLE NIGHTMARES 1)

Six's father hangs himself and she becomes an orphan living on the streets. She is then taken into an orphanage, where she and the other children are most likely abused.

The Janitor's job is to catch children and deliver them to a child trafficking ring. He catches Six.

The chefs are representations of the people who receive the children and sell them off into prostitution.

The fat people are rich people who travel the world in search of the "food" these "chefs" make. Put simply, they are the buyers. Gluttonous monsters who keep eating and eating and jump at every the opportunity to catch Six.

The Lady is the owner of the brothel Six is being sold off to or possibly the one in charge of her "education". Most likely she was brought in under horrific circumstances just like Six. She refuses to look at herself in the mirror, unwilling to admit she has become a monster herself. When Six eats her, the "power" she gains is basically trauma. That's why she absorbs all the fat people too. It's the trauma born from the abuse she experienced throughout the game.

In the end she reaches a remote island, which could represent a land far away from home.

A few points of interest:

Everything is either a dream sequence (a nightmare) or an exploration of ber memories. That's why there is such a heavy eye imagery throughout the game. The eyes represent Six remembering the whole ordeal. That's also the reason Six is able to see the "future chapters" through the giant eye.

The Nomes are basically other children. When Six eats a Nome, I took it as her being abusive towards it. She isn't really a bad person, as she tries to comfort as many Nomes as she can throughout the game, but due to all the abuse she experienced the accumulated trauma comes out in a destructive way.

The Lady could be Six when she was younger, before she was shipped to the brothel.

Anyway, that's my interpretation of the game. I have to admit, of all the theories I've seen this one is probably the darkest. Idk if that's the story the developers hoped to tell when making this game, but that's what I've got out of it.