Don't most state consitutions provide language similar to the 2A but at the same time preserve the state's right to regulate concealed weapons?
I don't know. The critical question is whether the language of such constitutions presupposed they had the power to legislate such matters, or like the 2nd Amendment presumed it was already an inherent right beyond their interference -- at the time the Bill of Rights was ratified.
Most have some provision. Some only mention the militia, some don't mention it at all. Many post civil war Constitutions allow for regulation (which has historically meant banning) concealed carry. In other states concealed and open carry of handguns is or was banned, even without such a Constitutional Exception. An example would be Nebraska (before they passed CHL at least). The state Constitution then read:
"All persons ... have certain ... rights, among these are ... the right to keep and bear arms, and such rights shall not be denied or infringed by the state or any subdivision thereof.” Then the people, in 1986, modified the Constitution to read:
"All persons ... have certain ... rights, among these are ... the right to keep and bear arms for security or defense of self, family, home, and others, and for lawful common defense, hunting, recreational use, and all other lawful purposes, and such rights shall not be denied or infringed by the state or any subdivision thereof.”
Yet the state courts have never thrown out a gun law on the basis of the state constitution, which originally made it clear that the right belonged to "persons", and was modified to make it clear that "all lawful purposes" were protected. So much for checks and balances, as well as the will of the people. Politicians don't like people owning guns, even in a rural generally socially conservative state like Nebraska, and will restrict, ban and confiscate them at all opportunities, at least as long as they do not pay politically or otherwise for doing so.
There are 6 states that don't have a clause that would equate to the 2nd amendment. California, Iowa, Maryland, Minnesota, New Jersey & New York are the states that don't.