At what point was it at its most common, and at what point did it stop? Or is it mostly an overblown stereotype?
This question dedicated to /u/Sakarabu
I cannot fully answer this but I do want to make a methodological point: whose measure do we use? Medieval society had a much more stringent interpretation of what constituted consanguinity than we do today. Can you work out if you are related, or your parents, are sixth cousins? If your families haven't moved significantly far from your region in a few centuries then it is fairly possible that your marriage would have contravened canon law.
In the medieval period, and especially among the nobility, potential pairings were indeed much smaller, socially, geographically, and politically which meant that incestuous pairings had to be made. Nobles could and frequently did make applications for papal dispensations to marry fourth or fifth cousins - or they just went ahead and if they were displeased with their spouse they used consanguinity to absolve the marriage.
If you are interested in medieval marriage you might want to check this earlier thread or do a search as I'm sure the topic has come up before.