Witch Hat Atelier spoilers

Because while the obvious purpose would be that it protects against anyone seeing potential manifestations of the silverwood, that doesn't explain why he starts wearing it as a kid before he or anyone would have known about the silverwood. So I think the top is something that has come to serve multiple purposes throughout his life. AND I think it has an important role to play related to the one silverwood attribute that it seems like a lot of people skip over: it heals injuries in its host (to allow them to escape to "safety").

When he was a child, I think the black top was devised as a solution to cover the wounds and scars from his abuse and captivity. While it's hard to see in the illustrations that there's any obvious neck wounds, his wrist is clearly shown as marked by some kind of bondage (Beldaruit's flashback in ch. 36)--which is also why the thing extends so far onto his hands. It makes sense that as a child he would be self-conscious about these obvious scars, and so the garment was created to allow him to have freedom of movement with the most coverage.

With the revelations of the silverwood, I think the meaning changes. First, because obviously now there is the potential for someone to see its growth on him, but ALSO because when it does manifest, his wounds and scars are erased. This is what we see at the end of ch. 93 when he walks into the lake--not just that gazing at Olly has activated the silverwood, but that in being activated, it is erasing the scar left from the Romonon injury on his shoulder. If anyone were seeing Qifrey's body regularly, the sudden disappearance of scars would obviously be incredibly suspicious. I personally imagine the first major Silverwood incident at the Tower of Tomes is what erased the neck and wrist scars--but he couldn't ever let anyone know that. Any time he is seen without the layer is a potential risk for questioning.

(This is also why I think fics/fanon that describe his body as scarred are wrong. The eye wound remains because the eye can't be replaced, but there's a reason why the silverwood always starts there--that's the injury it's trying to heal. Otherwise though, Qifrey should actually be unsettlingly unmarked by all his injuries).

Finally, on a more meta level, the fact that the top is there to cover nothing--that is, not the presence of something but the absence, is fucking genius. I'm sure like many of us, when I was first watching/reading WHA I assumed that the layer was covering some kind of glyph or magical marking on his body, considering how much that was signaled as the ultimate wrong in the early parts of the story. If not that, then yeah, maybe some kind of scar. But then when we finally see him stripped of it, there is nothing.

This is paralleled by the hair/black lens used to cover the lack of his right eye. It's hard not to see this as Shirahama's direct response to the (especially shounen) anime/manga trope of the character with a hidden "magical eye." There's obviously the Kakashi-type, and Lelouch from Code Geass, and a million others I'm suddenly blanking on. But the trope is predictable: ooh, can't see this guy's eye, must be some kind of taboo magic, etc. etc. So again, in the same scene where we see him without the black top, we also see him without the glasses, and all that's there is... nothing. Not some scary powerful forbidden magic eye but just a horrendous and heartbreaking injury, a total absence.