Word Usage – Meaning of ‘Wither’ in Context: ‘Wings Sprouted from Each Wither’

The "standard" spelling is

Scary-looking thing, isn't he?

I'm not entirely sure, but I believe this kind of spelling is called "eye dialect":

Eye dialect is the use of nonstandard spelling for speech to draw attention to pronunciation. The term was coined by George Philip Krapp to refer to the literary technique of using nonstandard spelling that implies a pronunciation of the given word that is actually standard, such as wimmin for women; the spelling indicates that the character's speech overall is dialectal, foreign, or uneducated. This form of nonstandard spelling differs from others in that a difference in spelling does not indicate a difference in pronunciation of a word. That is, it is dialect to the eye rather than to the ear. It suggests that a character "would use a vulgar pronunciation if there were one" and "is at the level of ignorance where one misspells in this fashion, hence mispronounces as well".

The term is less commonly also used to refer to pronunciation spellings, that is, spellings of words that indicate that they are pronounced in a nonstandard way. For example, an author might write dat as an attempt at accurate transcription of a nonstandard pronunciation of that. The rest of this article will discuss the former definition.

(Wikipedia)

There's likely a technical point here I'm unaware of. Anyway, at the very least, the point of this spelling is to show that he speaks very differently from the others. I imagine it possibly reflects a real-world dialect, but I wouldn't know which one.

It's a made-up word. It has no meaning.

From Muggles' Guide to Harry Potter/Magic/Blibbering Humdinger at Wikibooks:

No description of the Blibbering Humdinger is ever given to us. From the fact that only Luna Lovegood seems to believe in its existence, we can safely assume that it springs from the fertile imagination of Xeno Lovegood, her father.

The Blibbering Humdinger is first mentioned in Harry Potter and the Order of the Phoenix when Luna Lovegood says that people used to think that they didn't exist. Hermione replies that they were right, because they didn't exist, causing Luna to slouch off, annoyed.

In Harry Potter and the Deathly Hallows, after the Battle of Hogwarts, Luna, seeing how tired Harry is, distracts the people around herself and Harry Great Hall by saying, "Ooh, look, a Blibbering Humdinger!" This allows Harry to don his Invisibility Cloak, and collect Ron and Hermione without anyone noticing.

Although it has no meaning, it might have been a play on words intended to convey the same kind of meaning as gibbering or blithering, which it sounds like a combination of. From both gibber and blither, respectively:

[Merriam-Webster]
: to speak rapidly, inarticulately, and often foolishly
: to talk foolishly or nonsensically : BLATHER

But that's purely speculation on my part.

Hermione's comment is mainly meant as a snide comment, referring back to her statement that no such creature exists. (But the syntax makes it sound as if blibbering is something that a humdinger does.)