] marriages between first cousins generally have ......twice that small chance of producing unhealthy offspring. Shoumatoff relates how geneticist Bob Williamson suggests that each "normal" person may carry "twenty or so potentially lethal recessive genes, from whose lethality we are protected by also carrying a healthy, dominant version of the same gene." Marriage between close cousins definitely increases the chance that one of these recessive genes will pair up with itself; that is, that two genes, identical but passed down through different family lines from a single common ancestor, may double up and produce the unhealthy trait in a child of close cousins. First cousins, who may hold about 1/8 of their genes in common, may be somewhat concerned about the possibility of a harmful recessive gene in their common ancestry, particularly if they know that one exists
(from HCs link above on first cousins)

So as Emma and Isabella's children would be double first cousins with twice the usual amount of genetic material in common. They would hold 1/4 of their genes in conmmon and be four times as likely as unrelated people to have unhealthy offspring if they had children. Not to mention the fact that for this reason their marriage would be specifically forbidden in North Carolina! (Although apparently not forbidden in the UK)