The Second Amendment definitely is talking about weapons of war because it's clearly dealing with militias at minimum. When it's saying "well-regulated militia," at minimum it's talking about something like common citizens gathering every month with their muskets to practice drills in the town square. Sometimes they supplied the musket for you, other times you had to buy it and the price of the gun was considered a legitimate tax on the person. That phrase "well-regulated" meant not only regular meetings and discipline, but weapons meeting specific standards for military suitability. It was to make sure the community had functional military weapons. They were citizen soldiers.
Those muskets were weapons of war. They had to meet minimum standards to make them suitable for warfare or you got legal punishment. To ensure compliance, your musket, and the bayonet, balls, powder, flints and so on, was to be inspected and legal action taken if things were not in working order.
Having a musket suitable for military service was a civic duty and a public obligation, in addition to being a right of the citizens (see the English Bill of Rights). It's an odd thing but gun regulation, was not so unusual in the early days, but it was to make sure you had weapons capable of lethality. The regulation promoted gun possession.
The founding fathers clearly had no problems with an armed citizenry. They looked at things in terms of a musket in the home of every able-bodied male. Their vision was exactly what we say: honest, law-abiding people with guns safeguard and watch over public safety and deter evildoing.