I have been reading about Bill and Fleur's wedding in DH, and we hear about a lot of people with red hair who are presumably members of the Weasley family. We know that Arthur has two brothers (though we know Bilius is know to be dead), so how many members of the Weasley's extended family can there potenitally be? Cousins and the like?
We also know that Molly had two brothers, but they were both killed because of their involvement with the Order. But does she have any other siblings, do you think, or would they have been mentioned?
And how does this Aunt Muriel fit into the Weasley family?
I don't think Molly has any other siblings. JK would have mentioned it when she talked about Molly having two brothers.
The mention of other Weasley cousins is interesting because none of them appeared to attend Hogwarts. So they either have to be much older that Ron, or much younger.
There was supposed to be a girl cousin who was the child of Molly's Squib second cousin. Mafalda was supposed to join in GoF and be Sorted into Slytherin, but JKR changed her mind and substituted Rita Skeeter instead.
Aunt Muriel - I think she could well have been a great aunt to Ron. She's obviously much much older than Arthur and Molly so not a sister to them. TBH, the way she talks disparagingly about the Weasleys I think she's from Molly's side ... but possibly not a Prewett.
"Weasley cousins" could always be cousins of Mr Weasley, for example, too, or second/third/... cousins. Like, the children of Arthur's cousins. Maybe "cousin" is just a term for "some sort of relative" here. The family is large...
And there are other factors, like - we don't know how old Molly's brothers were. It's possible that one of them already had grown children when he died.
There can be hundreds of them, really. Judging by Aunt Muriel's comment, the Weasleys in general (not just Arthur's family) tend to have a lot of children.
I know from genealogical research that for one thing, people in general call people cousins when they seem to be related in some way, even if they aren't actually related, or even if the relationship is actually something else.
For example, one person I call a cousin is actually the daughter of my grandmother' s brother. She is my mother's first cousin. What exact sort of cousin or aunt or whatever she is to me I don't know and frankly, couldn't care less. So basically I think it is entirely credible to include as "Weasley Cousins" anyone who, by marriage or blood, could possibly be connected to the Weasleys, if that helps your plot along.
Also, even a female cousin of who had married and no longer carried the Weasley name might, if she were proud of her birth family, still consider herself a "Weasley" and consider her children Weasleys as well as whatever their names actually were. Using this logic, there could be Weasley cousins we've heard mentioned, but did not realize were related. While technically this might not be considered "correct," it is something people do.
As for the cousins thing, I'm pretty familiar with large families - I'm one of twelve on my dad's side, and three on my mother's - but both of my parents were one of five, and my father's parents had sixteen and twelve siblings among them. Sometime along the way, one of these cousins calculated that my father and his brother and sisters had over one hundred first cousins - even as that number continued to grow.
As I understand it, relationships go as follows:
Susie marries Jim, who has a brother Matt, who marries Lauren
Susie and Jim have a daughter - Ashley
Matt and Lauren have a son - Patrick
Ashley and Patrick would be first cousins.
Lauren and Matt would be Ashley's Aunt and Uncle.
Susie and Jim would be Patrick's Aunt and Uncle.
Ashley marries David; they have a daughter Betty
Patrick marries Carol; they have a son Michael
Patrick is Betty's first cousin "once removed" - they are not of the same generation
Michael is Ashley's first cousin "once removed".
Betty and Michael would be second cousins. - they are of the same generation, but their parents are cousins, not siblings.
Jim would be Michael's great uncle - his father's uncle - on the same generation as his grandfather.
Betty marries Ed; they have a son named Xavier
Michael marries Nancy; they have a son named Paul
Paul and Xavier would be third cousins. - same generation, parents are second cousins.
Betty would be Paul's second cousin "once removed" - again, they are not of the same generation.
Does that make sense? So "cousin," while it is often used colloquially as just "a relative of mine," can also literally mean cousin - though by which degree would depend upon the actual relation.
As to the Weasley family, I think likely it is that Arthur had some cousins who had children - they would be Ron and Ginny's second cousins. As to why they were not at Hogwarts, we don't hear of any siblings of Arthur's having been between his age and the Marauder's age, so I think it likely that he was one of the youngest of his generation - his cousins kids might be much older than his own, perhaps with young - but not school-aged - children of their own. Or at least that was my interpretation of their absence.