Just for the hallibut, I started poking around in 19th century newspapers to find out how people a little closer to the Founding Fathers felt about carrying concealed weapons. It was not an issue in the 18th century; as far as I know, it didn't even come up. Handguns were expensive and therefore rare. I suppose it's possible for a very tall man to mostly conceal a flintlock rifle, but it never really caught on.
Handguns were around, but didn't start to appear in significant numbers until Samuel Colt started successfully mass-producing them in the 1840's.
To read the papers, I went to the Library of Congress's catalog of online historic newspapers, Chronicling America. The catalog only goes back to 1836, and it would be nice to have gone back further, but because of paragraph two, it didn't really matter that much.
I performed a search on the phrase "concealed weapon," and asked the search engine to sort them by date.
The first reference that popped up was in an 1838 copy of the Bloomsburg, Penn., Columbia Democrat:
In 1853 the Hannibal (Mo.) Journal didn't think it was such a good idea.
This was the only article I found – though I am sure there are many more – which seemed to suggest that making carrying a concealed weapon illegal was a good move, and I include it for that very reason.
Here are some other articles I found. The Loudon Free Press, in Loudon, Tennessee; May 6, 1853:
Also from Texas in 1879: