If I owned Harry Potter, something so scary as this wouldn't happen.

Originally researched from an offhand comment "half the students will be redheads or Potters, or both". Rewritten for more coherence, math has been re-done as well. There is a new funny scene at the bottom.

Out of the 172 'Wizarding Families' 83 are viable (not extinct, out of the country, or in jail) when Harry's generation becomes adults. One is the Weasleys, one is the Longbottoms (related to the Weasleys) and one is the Potters (marries Weasley). So, how long would it take before everyone is related to the Weasleys?

In Harry's Generation, 80 families are not related to the Weasleys, and three are.

I know this is a simplification, since Muggleborns will be constantly joining, and some families will have been related previously to each other, and some having more than two children clouding up the gene pool. Not to mention only children who didn't reproduce and ended their line. Let's assume that the Muggles and Muggleborns entering the society are just enough to cancel out the inbreeding that I'm not tracking Since there is not clear information about how many Muggleborns are in Harry's year (9?) or later years, and also not enough information on which families are related to each other or how closely, other than a few offhand comments, we'll ignore both previous degrees of relation and future muggleborns.

We'll assume that every family has two Wizarding kids, to replace the parents. Not every WR person is going to marry a wizard, but, honestly, how many will marry muggles? It happens, yeah, but look at how many 'halfbloods' are from muggles vs. muggleborns. All the WR kids will be marrying wizards in this model.

Math is Non-W minus new Weasleys for tentative total for NW remaining in Britain. Everything is rounded up. No half-people. For the extra people that come from this rounding, pretend that WR: two kids from that family married WR, NW: Had more than two kids.

Generation

HG WR-3 NW-80 80-6(WR marry outside WR, no inbreeding!)=74

G1 WR-6 NW-74 74-12=62

G2WR-12 NW-62 62-24=38

G3WR-24 NW-38 38-48…Wait. Ten of those kids can't marry wizards

One Big Happy Family…and a few Muggleborns.

4 generations, the legal amount of time before a family can intermarry, according to google, came too late for the Wizarding world. The majority of the Wizarding world is 3rd cousins or closer to one another, barring muggleborns, and those extra children we didn't count. Then again, there were 7 Weasleys, plus Longbottom. We only counted Harry/Ginny, Bill, and Ron/Hermione. And we KNOW the first pair had more than two kids.

"Harry!" recognizing the voice as Bill's oldest daughter's niece, Harry turned around with a smile. Only for it to fade as half of the platform crowd turned with him. Why did all of his classmates have to name their kids after him? Half of his grandkid's classmates had been some version of Harry, James, or Lily. The other half were redheads. Apparently, Weasley Red was a dominant color.