Read the Constitution. It gives the federal government clear jurisdiction over commerce between the states. You can argue whether SCOTUS has over expanded that, but you can't argue that it doesn't exist. Well you can, but you won't have much luck with it. ATF has jurisdiction when arms or ammunition are moved across state lines. That's why there are some moves by states in the west to write laws regarding arms and ammunition made within their borders. What success they'll have is anyone's guess.
It gives them jurisdiction to REGULATE it. I.e. make regular and prevent states from tariffing each other.
At least that was the intent. Subsequent generations altered the meaning of the word regulate to mean restrict. It meant no such thing in 1791.