In the 1700s and 1800s, royalty in europe often married their close relatives; furthermore, recessive genetic diseases such as hemophilia showed up much more often among royals than in the general population. explain the likely connection.

Well, first off that's gross.
The recessive gene showed up more in the royalty because if a close relative such as a first cousin would carry the same genetics as the spouse, because likely the grandfather or grandmother had the disease. The commoners would not do that because they are marrying in the family.