Well, I told you where it comes from (at least in Central Europe), it is in the town charter. I didn’t see where you had made the distinction between ubiquitous in the 16th century and unheard of in the 14th.
I guess before going to look for primary sources (?) for the 14th Century I would counter your question with another – once the towns had walls and militia, who was going to dictate to them whether or not their citizens could bear arms or anything else? Seeing as they routinely defied kings and emperors on any number of policies (right up to and including fighting pitched battles against them), and were governed by their own citizens, the only thing which could prevent citizens from bearing arms or exercising any other rights would be a very strong internal monarchy or dictatorship of some kind. So far as I know these were pretty rare north of the Alps, though in Italy you did have some Condottieri taking over towns. This is how the citizens of Milan lost many of their rights for example.
Give me a bit and I’ll find some sources, it’s been a while since the idea of armed burghers was an issue in any discussion I’ve had, I’ll have to find some old stuff.