The quotations from the 1700s were about a time in which most people lived in rural areas, with Indians & wild animals and hunting as a major means of support.

When defense of the new 'country' was involved. they NEEDED every adult male who could obtain a weapon... and the weapons were non-standard, usually hand-made. Conscripted or volunteer soldiers needed to bring what weapons they had. It was almost 100 years before the army was able to standardize and issue weapons in any number.
The 2nd amendment and the views of the founders were written with that situation prevailing. When the demographics and the technology changed, the constitution and the attitude did not. Everyone who liked or was seriously involved with guns interpreted the Constitution to mean "You can STILL have almost any weapon you can get a hold of 'legally'"... as if frontier rules still applied.

As demographics & society and urbanization changed, so did rationalizations for why the 2nd Amendment should not be changed and should be interpreted as freely as possible. (I still believe that the 2nd Amendment should be held to read that "the people when in a militia...or army should bear arms"...but we see how THAT idea is treated by the NRA...etc.