To all passionate shippers out there:
We know (sort of) that they both have been experimented as children. While we know what was used on Olivia, and do not precisely know why, we still have not been told clearly what has been used on Peter.
But I have a guess why: Walter never cured Peter. Instead, he developed a treatment, for lack of a better word, that made him important. Indispensable. He created a treatment that made the Observers preserve him.
The clue for my theory is in episode 2.8, where he tells August that the only way for the girl to survive is to make her important. (And be prepared to face the consequences)
In a later episode Walter mentions that Peter's illness miraculously disappeared. Genetic diseases do not disappear miraculously.. (It is why William Bell said that Peter was holding up better that he'd thought. It is why the first thing Walter did when he saw him at the mental ward was to check his eyes/vitals.)
This is what Walter did, and he remembers. But he's not telling anyone, at least not yet. He made the other Peter important, so he would not die as well. This is why Peter can operate the machine - Walter made him what he is. And that makes him uniquely linked to O. So, even if he enjoyed the fun FO, in the end, he's as dark, and as damaged, and exactly as un-fixable as Olivia. My guess is, once he finds out (a back-into-the past episode is coming up soon), it would bring them closer than anything before.

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