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Recently I've stumbled across China Miéville's novels. Apparently, they fit in a genre called Weird Fiction, or to be even more specific New Weird, where the "new" is used to distinguish new writers from literary sources as Lovercraft.

Yet, in my opinion, a book like Perdido Street Station could be defined as a crossbreed between fantasy and steampunk. In short, I'm having trouble understanding what the "New Weird" as a genre entails.

From the Wikipedia page enter link description here a bunch of definitions can be found:

... according to Jeff VanderMeer and Ann VanderMeer, in their introduction to the anthology The New Weird, the genre is "a type of urban, secondary-world fiction that subverts the romanticized ideas about place found in traditional fantasy, largely by choosing realistic, complex real-world models as the jumping-off point for creation of settings that may combine elements of both science fiction and fantasy"

However,

Robin Anne Reid notes that while the definition of the new weird is disputed, "a general consensus uses the term" to describe fictions that "subvert cliches of the fantastic in order to put them to discomfiting, rather than consoling ends". 1 Reid also notes the genre tends to break down the barriers between fantasy, science fiction and supernatural horror.

And then again, from a more historic point of view:

Part of this genre's roots derive from pulp horror authors, whose stories were sometimes described as "weird fiction".

My point here being that there is not a specific consensus on this. So, a new author wanting to write a Weird Fiction novel will either find himself expanding the definition or missing it completely.
After all, other genres can be see as a breaking of barriers between fantasy and science-fiction (as Steampunk, maybe) or fantasy and horror (dark fantasy or grimdark).

So, what would be the most important characteristic, the one that you absoulutely cannot miss, when writing New Weird?

Genre should be seen largely as a way of connecting a writer with the audience most likely to enjoy his or her book based on elements shared with other books. It isn't an exact science, and for this, a hybrid subgenre, you'll be looking for a signature combination of traits, rather than a single defining one.

I'm not previously familiar with the label "New Weird," but it seems quite clear, and I can readily identify work I've encountered that would arguably fall in that (non-exclusive) category (Dreams of Shreds and Tatters, Coyote Kings of the Space Aged Bachelor Pad, Sandman, Black Mirror, Kafka on the Shore)*. If I had to redefine it, I'd call it

Contemporary magical realism, but with a horror-influenced sensibility.

It needs to feel fresh and new, not old and musty. It needs to have supernatural or science fiction elements, but it needs to combine those with a realist setting, not a fantastic one --it needs to give the sense of strange things intruding into the real world in which we live, rather than transporting us into an escapist world. Finally, it needs a mood that is dark, eerie, disturbing, cautionary or horrific, not one that is twee, playful, childlike, mythic, wish-fulfilling or reassuring.

* Note, I'm not much for horror, so my examples are probably on the lighter end of this spectrum.

If 'new weird' is a reference to the Weird Tales of the likes of HP Lovecraft and other writings in the Cthulhu Mythos, I would imagine the primary trait of New Weird would be application of the fantastical in a way that implies it's incomprehensible, malevolent, unknowable and dangerous, rather than empowering, whimsical, et cetera.