First Reaction, I did't think same sex incestuous marriages were allowed in the 16th century . . .
Second thought, brain kicks in, perhaps an heir is produced, which then becomes King or Queen supplanting the Stuarts
Barring Buterflies
Catherine's oldest son Edward Seymour ascends the throne in 1603
Edward VII 1603-1612
Edward VIII 1612-1618 (Died without issue)
William III 1618-1660 (Edward's Brother)