I think when Malowebi asks Meppa what he is and he replys, "Weary". Says a lot about Kellhus's human nature.
You might be reading too much into this. When he returns to Momemn in The Judging Eye (or was it WLW?) to see Psatma Nannaferi, he's exhausted purely because of the exertion of travelling that distance by teleportation. And that journey was much shorter. I think he was simply tired because of that.
While that is plausible, why say "weary" when he meant "tired" or "exhausted." No, to me weary has a whole different connotation than either of those others and so it seems wholly reasonable to draw the inference that MSJ did from his choice of words. Being weary isn't just being tired.
This.
Also, I'm not buying anything we see of Kellhus that doesn't come from his own POV. He never stops dissembling. Ever. And we as readers only get the perspective of the POV character, only ever able to *guess* at what's really going on in his head even after 6 books.
ETA: also, Kellhus want really tired after travelling in TJE. He just pretended to be too manipulate Esme. He always makes an effort to appear at least somewhat human with her so that she will stay in her place.
You are the fist that beats us.