They're not actually shown to be more blood traitorous than others
I think the answer to this question may be that its premises are not entirely correct. If we look through the books we don't actually find that the Weasleys are specifically targeted with the blood traitor stigma.
There are only two other people that are explicitly referred to as blood traitors in the books:
"Yoooou!" she howled, her eyes popping at the sight of the man.
"Blood traitor, abomination, shame of my flesh!"
"You disgusting little Squib, you filthy little blood traitor!"
roared Gaunt, losing control, and his hands closed around his
daughter's throat.
The Weasleys are mentioned as blood traitors a little more than a dozen separate times. However, we have to account for selection bias here. Even if there were a hundred other families that were as equally blood traitorous as the Weasleys, we would expect to hear it much more about the Weasleys because the Weasleys are main characters. Since we are exposed to them all the time throughout the books it is logical to assume that we would hear about their traitor status much more than we would hear it about other peripheral characters.
For example, the majority of mentions of the Weasleys being blood traitors are the ravings of Kreacher and the portrait of Mrs. Black. This is perfectly understandable because the Weasleys are the blood traitors that are always present in Grimmauld Place (or at least present whenever the reader is present).
Similarly, there are a few other mentions that are perfectly understandable in this light:
- Slytherin Seeker Harper refers to Ron as a blood traitor.
"Thinks he's something special today, doesn't he?" said a snide voice,
and Harry was nearly knocked off his broom as Harper collided with him
hard and deliberately. "Your blood traitor pal..."
This was not a conversation about blood traitors. It was simply a Slytherin trying to annoy Harry and insult his best friend so he used the best insult a Slytherin could come up with and called Ron a blood traitor. If Harry had happened to be best friends with someone else who came from a family with pro-Muggle leanings, Harper likely have said the same thing.
- Zabini calls Ginny a blood traitor.
"I wouldn't touch a filthy little blood traitor like her whatever she
looked like," said Zabini coldly, and Pansy looked pleased.
Here, too, it was not a conversation about blood traitors. Zabini was simply explaining why he wouldn't like Ginny no matter how good-looking she was. To that end he says the most negative thing about her he can think of, namely, that she is a blood-traitor. Had they been talking about a different girl from a pro-Muggle family, he would probably have said the same thing.
- Pius Thicknesse refers to Mr. Weasley as a blood traitor.
"Ah, well. It's only a matter of time," said Thicknesse. "If you ask
me, the blood traitors are as bad as the Mudbloods. Good day,
Runcorn."
Once again, this was not a conversation about blood traitors. It was a conversation about Mr. Weasley, and Thicknesse was merely expressing his opinion of him. Had they been talking about someone else, Thicknesse would likely have said the same thing.
- Fenrir Greyback refers to the Weasleys as blood traitors.
"A Weasley?" rasped Greyback. So you're related to blood traitors even
if you're not a Mudblood.
Here as well it was not a conversation about blood traitors. Greyback was just mentioning the fact that a prisoner that he caught is related to blood traitors, which may be something he would get rewarded for.
- Bellatrix calls Ron a blood traitor.
"If she dies under questioning, I'll take you next," she said. "Blood
traitor is next to Mudblood in my book.
This too is not a conversation about blood traitors. Bellatrix is simply using a standard pure-blood insult, and explaining why she would pick Ron next.
In short, the reason it seems like the Weasleys are targeted so much is merely that, as the readers, we are hanging out with the Weasleys so much.
Note that in all of the above instances, the "bad-guys" never stated or implied that the Weasleys are more blood traitorous than any other blood traitors.
This brings us to the three statements made by the "good-guys".
Sirius says:
But there's no point looking for them on here — if ever a family was a
bunch of blood traitors it's the Weasleys.
And Ron says:
"My whole family are blood traitors! That's as bad as Muggle-borns to
Death Eaters!"
And he says:
"It was always a matter of time, Dad's been saying so for months.
We're the biggest blood traitor family there is."
Here we finally see the perception that the Weasleys are somehow especially blood traitorous. However, there are several points to make. Firstly, these are the "good-guys". They may not be accurately informed as to how the "bad-guys" rank their blood traitorousness.
Secondly, they may be simply exaggerating.
Most importantly, though, even if they are correct and literal, the particular egregiousness of the Weasleys' blood traitorousness may not be that they are worse blood traitors, but simply that there are more of them.
Any pure-blood family can have one bad apple. When they do, the family can simply blast them off the family tree and forget about them. But with the Weasleys its not just one deviant family member who challenges the pure-blood beliefs. Its the entire family (clan?) that rejects them. Thus, the Weasleys are somewhat unique in that they are a whole group of blood traitors, even if there traitorousness is not inherently worse than anyone else's.
In each of the three above quotes, it is specifically mentioned that they are a family of blood traitors. This may be the reason — if it is true at all — that the Weasleys are looked at as different from other blood traitors.