The Weasleys are not pure-blood.
The concept of "pure-blood" in the Harry Potter universe refers to witches and wizards whose families have only magical ancestors for generations. The Weasleys, however, have a history of intermarrying with Muggle-born witches and wizards. This fact is explicitly stated in the books, particularly in Harry Potter and the Half-Blood Prince.
Arthur Weasley, the patriarch of the family, is a strong advocate for the acceptance of Muggle-born wizards and witches. His wife, Molly, also demonstrates a similar acceptance. This family's dedication to inclusivity and their opposition to prejudiced views like those held by the pure-blood supremacist group, Blood Purity, solidify their stance against the idea of pure-blood superiority.
The Weasleys are a prime example of how the concept of "pure-blood" is a fabricated notion used to create a hierarchy and foster discrimination within the wizarding world. Their acceptance of individuals from all magical backgrounds highlights the arbitrary nature of this system and emphasizes the importance of inclusivity and equality.