The prize for most eerily plausible Game of Thrones fan theory of the moment goes to Reddit user catNamedStupidity. Arya Stark fans may want to turn back now, because if this theory is true, Arya as you know her would be no more. According to the theory, Arya and the Waif are the same person. And not in some sort of weird time travel way — they are literally the same person, with the Waif only existing in Arya's mind. You just got chills, didn't you?
The Fight Club-style theory posits that Arya is experiencing a bit of a dissociation. The Waif is the "no one" Arya is trying to be, while Arya herself is the only thing standing between her reaching her ultimate goal of joining the ranks of the Faceless Men. According to catNamedStupidity, the evidence in support of the theory is how the Waif is only ever seen by Arya and Jaqen H'ghar, she knows everything about Arya, including her location at all times, and she tries to taunt Arya into leaving by constantly challenging her.
I think it would be safe to say that the Waif believes Arya to be weak because she cannot fully let go of her identity. It makes a strange sort of sense that Arya would deal with the push and pull between being Arya Stark of Winterfell and being no one by inventing an adversary in her mind. Given the magical nature of the House of Black and White, Aya could have no idea that the Waif does not exist.
The most compelling piece of evidence comes from the fight scenes between the Waif and Arya when Arya was blind. Now, I don't know how people roll in Braavos, but generally speaking, most people would try to help a blind girl who is getting her butt kicked. At the very least, the scene would turn a few heads. However, if you rewatch the fight scenes, no one in the streets reacts at all to what is going on.
What's more, Arya is never visibly bruised after these brutal fights. She has a bit of blood on her lips and nose, but those are injuries that would be expected if you faceplant on the ground enough times. Arya's fellow beggars could be ignoring her antics because they believe she is just a mad girl swinging a staff at thin air.
It is important to remember that Arya has always cycled through various identities. Since Ned's death, she has pretended to be a boy joining the Night's Watch, a cup bearer for Tywin Lannister, and no one at the House of Black and White. In the books, Arya tries on even more identities during her training with the Faceless Men, and rather than cover all of the different people Arya pretends to be, the show writers could have opted for just one separate identity during her training: the Waif.
In Episode 6, "Blood of My Blood," Arya appears to finally reject all of her training and reclaim her identity, retrieving Needle, the last piece of her old life she had not let go of. Meanwhile, the Waif asked Jaqen H'ghar if she could be the one to finish Arya off. The stage is set for a major battle between the Waif and Arya, but in actual fact, Arya could be on her way to completing her training.
If she is the Waif and the Waif "kills" Arya and disposes of Needle, then Arya would finally be no one, another nameless assassin whose only mission in life is to serve the God of Death. Like Jon, Arya may have to die in order to be reborn. If she loses the battle with herself, then she wins by finally letting her old life go.
Of course, this is all speculation, and the Waif could very well just be the last person standing in the way of Arya reclaiming her identity and heading back home to Westeros. Keep in mind though, that Episode 8 of Season 6 is titled "No One," which could be hint that Arya's time with the Faceless Men is just beginning.