Blood relatives who marry in this country would be shunned by most. This is a practice that is most definitely frowned upon not to mention illegal in most contexts.
We also need to think about the children that this couple may conceive. There are many problems they may have to deal with socially if and when others found out their parents were biologically related.
All good and valid points, but we might also recognize the societal stigma attached to those people who intermarry. Granted, the societal stigma evolved from the laws forbidding this that evolved from the scientific knowledge that genetic anomalies would result.
Though I agree with Pohnpei (I almost always do, he's a smart guy) I thought there were a few things I would add to the discussion.
First is your phrase "biologically related." Technically we are all "biologically related" as human beings. If you go back far enough you see the common "trunks" from which our individual branches sprout (for example, think of Europeans. They look different from Asians because of localized breeding, thus making them all "biologically related.") That's just a thought, though, nothing very new to the discussion.
What I wanted to add, though, was the sociological/psychological consequence of such a marriage. As far as I know, "modern" societies around the world do not accept people who are "blood relatives" getting married. And it's not just because of the possibility of "flipper grandchildren." Many close relatives who marry (think cousins) do not intend to have children...still, think of the stigma that these people have to live with. It's not just about the children. In our society, the concept itself is considered wrong by most people and those who engage in such relationships will generally be shunned by the society at large.
So, in addition to the consequences that might occur to offspring, consequences exist between the two individuals who might school to be involved in such a relationship. The attitudes of friends, neighbors, and other family members can make such a relationship a difficult proposition at best.
Post #2 makes a great point about the closer the relative the more likely a recessive trait will show up in the offspring. If the practice of marrying relatives continues over generations you run the risk of even more of those recessive traits coming to the forefront. If you compare it to what dog breeders do when trying to nreed a "better" dog they look for animals of completely different lineage and have the "positive" traits of the breed to breed with. While I understand that we do not look for lifelong partners so that we can breed the "perfect" offspring I think it shows the relationship between reproducing with a relative as opposed to a non-relative.
Historically, laws were passed in the U.S. and elsewhere that dissuaded some close biological relatives from marrying. In other world locations, however, these same laws didn't apply. Now close scientific study can confirm or deny some of our longheld beliefs. I found this MIT article on the topic especially interesting.
The typical problem with having children with a blood relation is that there is too much of a potential of having recessive traits show up as a result of inbreeding. This was famously true of all the royal families of Europe who inbred and became hemophiliacs. As far as I know, there's no magic line for "here's where problems start." I believe there are two rules: the nearer the relationship, the more danger and the more generations of inbreeding, the more danger.