Correlation between genetic distance and birth defects
For humans the closest argument may come from observational studies (since experiments aren't possible due to ethical reasons).

One example for the correlation of genetic distance and "defects" comes from a recent study of Chagnon et al. PNAS, 2017 http://www.pnas.org/content/114/13/E2590.full . Rather than asking for birth defects directly they however survey the number of children, and survival of children to age 15 (which would be one example of the term "inbreeding depression" that is more general than "birth defects")

Note that their study also sheds some light on the underlying big question, why certain types of kin relationships can be common despite their effect on the creation of healthy offspring - and why certain types of cousin relations are different from others.