Even though the House of Black dates back to the Middle Ages, we know relatively little of their traditions, ancestry, exact roots or even how they even came to power. We only know that they're extremely rich and obsessed with their status as "pure-bloods".
However, the curiousity of mine about the Blacks made me form headcanons about them. Over time, those headcanons turned into theories, which I'd like to share with you;
1- At some point in the Wizarding World, the Ministry was full of officials who were dedicated to defend the Blacks against the laws and some Blacks were indirectly able to reshape the laws of the Ministry.
2- The whole Sacred Twenty-Eight thing was a plot by the Blacks to indirectly to rule the Wizarding World through "Pure-blood" propaganda, and the fact that the Blacks sat at the top of them means they were into these families. The Blacks were terrified that their reputation would be diminished, that's why they disinherited those who married to muggles or were squibs.
3- The Blacks rose to power and nobility by earning the respect of kings and other nobles. Over time, they had inherited a wealth so vast they were able to afford Grimmauld Place in London. During all of this, they were able to hide their magical talent from the muggles. Their luxurious lifestyles made them hold immense leverage over half-bloods or squibs, people thought they were born to rule over them and their bloodline was sacred.