How is it possible that the Weasleys in the Harry Potter universe — are poor?
Most likely, Rowling didn’t pay enough attention to cogent world building. She told a great (7 great) stories, and that’s was enough.
Specifically for the Weasleys, of course they wouldn’t want to be poor, or seen as being poor (“Let me guess, hand-me-down robes… you must be a Weasley!”)
A true, cogent Potterverse would not support such income disparity — magic would cure this for everyone. And specifically for the Weasleys, as clever as they are (all of them, in fact), they would have figured out how to grow their wealth.
But Jeanne needed a poor, put-upon family, so, there you have it.
I’d say that Potter magic, above all magics in fiction, would be the least likely to harbor poverty, however one measures it. It’s just too easy to use magic, in some way, to better one’s life-style.