Inbreeding

"Marvolo, his son, Morfin, and his daughter, Merope, were the last of the Gaunts, a very ancient Wizarding family noted for a vein of instability and violence that flourished through the generations due to their habit of marrying their own cousins."

— Albus Dumbledore.

Inbreeding with pure-bloods is a common practice for elite wizarding families that uphold the tradition of marrying only pure-blood wizards of respected ancestry. It is noted that wizarding families are becoming more diverse as time passes as wizards begin to marry Half-bloods, Muggle-borns, and Muggles. To keep with tradition in maintaining a purely wizard-blood family, families tend to marry within the family, particularly cousins. 

The Black family

The House of Black's family motto had always been "Toujours pur", which meant "Always Pure". Therefore, the family was strictly traditionalized to marry, if not extremely wealthy as their own family, respectable and noble families. The Black family took this motto to heart very seriously, and all family members who did not conform with the obsession to the pure-blood supremacy were disowned quickly. Squibs were also disowned.

In desperation to keep with the tradition, some would go to extremes to keep the tradition. An example of this are Walburga Black and Orion Black. The two were second cousins, as both their grandparents were siblings, and had married to keep tradition and eventually had two children together. 

Due to the Black family tree tapestry large family tree of the Blacks, it is possible that related people marry or interact, not knowing of their relationship.

Inbreeding relationships

• Harry Potter and wife Ginny Weasley are third cousins.
• Arthur Weasley and wife Molly Prewett are second cousins by marriage once removed.
• Molly Prewett is the supposed niece of Ignatius Prewett (since being his niece justifies Sirius' statement that she is his cousin by marriage and not by blood, since being Lucretia Black's daughter would have made her cousins of blood) and is technically a distant relative of the Weasleys even before marriage.
• Harry Potter and his teacher Remus Lupin are first-cousin-once-removed-in-law.
• Harry Potter and his godson Teddy Lupin are first cousin twice removed.
• Victoire Weasley and boyfriend Teddy Lupin are fourth cousins once removed.
• Harry Potter and enemy Draco Malfoy are possibly second cousins once removed, as they might have the same ancestor, Cygnus Black II.
• Nymphadora Tonks and Draco Malfoy are first cousins.
• Neville Longbottom and Draco Malfoy are fourth cousins. 
• Harry Potter and Neville Longbottom are third cousins once removed.
• Ronald Weasley and Neville Longbottom are second cousins once removed.
• Ronald Weasley and enemy Draco Malfoy are third cousins once removed.
• Neville Longbottom, Ronald Weasley, Barty Crouch Jr. and Yaxley (the interrogator) could be related through the Black family.

Side effects of inbreeding

In Muggle genetics studies, it is proven that inbreeding can lead to serious problems, even for wizards. Notable effects that are seen in families are infertility (which would explain the extinction of the Black family) and disorders, both mental and physical. It is evident in many families (e.g. the House of Gaunt and notably insane Death Eaters of the Black family) that insanity is a common resultant.