So this question is sort of difficult to answer because of how radically different cities and cultures were during this era plus our limitations of gathering the sources needed to answer this type of question, but I will give it a quick go.

During the early 1770s, few Americans carried actual firearms around with them in everyday life because it simply wasn’t very necessary. However, many individuals who worked in some types of occupations would have objects with them that could be used as weapons that they used in their daily jobs. For instance, in Boston and other port cities which had industry that manufactured boats, it was quite common for the local men of the town to carry large clubs with them. These clubs were quite long and heavy, perhaps about the size of a baseball bat, and they were traditionally used to help create rope (which were needed for ships). Some of these clubs were used in instances like the Boston Massacre when the large crow who had gathered to harass British soldiers had begun waving their clubs and one actually struck a British Troop in the head. I believe The Shoemaker and the Tea Party: : Memory and the American Revolution by historian Alfred Young actually discusses this a bit when referencing the Boston Massacre.

When it comes to firearms, it was somewhat common for everyday people across many of the colonies to own personal firearms, especially if they lived in-land near Native American land. But in cities, I’ve never seen anything to suggest that people carried weapons around with them when simply walking around (I am not a firearms expect by any means, my specialty is religion and the economy, so I could just be missing the references to firearms here).

I’ve seen mixed reports on gun ownership during this time period and it appears that it is still something debated among historians for how many guns per capita were owned in each town. Regardless of the actual number, locals were well-armed enough to be able to create powerful militias in the early stages of the war using mostly their own rifles. How many did? Well, let’s look at the sources. In 1775, several states in New England tried to gather some surveyed data to understand how many guns were available, preferably for use in the militias. Surviving today are the records to six states that give us a small window into gun ownership during this era. Robert H. Churchhill actually conducted extensive research on this in 2003 with his article, “Gun Ownership in Early America: A Survey of Manuscript Militia Returns” [The William and Mary Quarterly, Vol. 60, No. 3 (Jul., 2003), pp. 615-642]. In this article, we are shown how gun ownership exploded through the American Revolution when local militias attempted to ensure that their militiamen were well armed. It’s probably reasonable to assume that in the early 1770s, less than a third of free white males owned firearms, but by 1776, that number had easily been doubled, with some people, like officers having a 100% personal gun ownership rate by 1776 in many American towns and cities.[pp626]

Hope this helped.