Never doubt the influence of natonalism on language development...
In England, as the influence of the Classical world was revived in the 15th century, scholars of English desired to remind their readers that most of the words in the language originated in Latin and Greek.
To show off their knowledge that ‘doubt’, then spelled 'dout' because it came into medieval English via French doute, was derived originally from Latin dubitare, they added the b — and it stuck. In its way, it was a nationalistic gesture, reasserting the (more prestigious) Classical origins of English over Dutch, French, German, and Norse influences of the intervening millennium since Roman influence waned in Britain from the fifth century and Anglo-Saxon languages began to infiltrate.
So, those in positions of power (read: printing presses) added in extra letters to words just because they could. In a time when language was far from standardized, this was a fairly easy feat to accomplish.
This can also be seen with "sign", which came from the same root word as "signature", so they kept the "g". Of course they also went rogue on occasion, as with "knife", of Germanic origin, where the "k" was indeed pronounced.