The founders, in 1808, appropriated funding for arms to state militias. [1]. Previously the arming of militias was up to the individual states. Some would have chosen to just have private citizens bring their own arms. Others would have actually set aside a fund to bring those arms.
And that's blatantly apparent when you think about the wars fought after the revolution. Cannons had to come from somewhere and you'd not expect a private citizen to have procured one.
That was, in fact, one of the reasons George Washington disliked the idea of militias, because you'd be arming untrained and undisciplined citizens with weapons they'd never used before and expect them to somehow know how to operate them.
> To place any dependence on the Militia, is, assuredly, resting upon a broken staff. Men just dragged from the tender Scenes of domestic life; unaccustomed to the din of Arms; totally unacquainted with every kind of military skill, which being followed by a want of confidence in themselves, when opposed to Troops regularly trained, disciplined, and appointed, superior in knowledge and superior in Arms, makes them timid, and ready to fly from their own shadows ... if I was called upon to declare upon Oath, whether the Militia have been most serviceable or hurtful upon the whole, I should subscribe to the latter. -- George Washington