Why would I make someone carry a weapon? JK, but never heard of such an expression.
Is this some kind of lingo they tell you about when you get a ccw permit?
"Make" is in reference to discovering them, finding out their secret.
Discovering an undercover officer would be similar.
You made the officer, you identified them undercover.
Like if you "made" a spy.
You discovered the spy, or someone else trying to hide an identity.
Or perhaps a security detail trying to keep a low profile, or investigator. You have observed some clue or presence that reveals an identity that the individual has tried to conceal.
The term has come to be used by people to describe discovering others carrying concealed, because by obtaining a permit they have become aware that such a world of people carrying guns in everyday society exists.
Of course blowing their cover for no other reason than just to demonstrate your self perceived superior skills of observation often shows a lack of maturity.
But some don't realize that and think it creates a comradery, identifying another special member of the 'concealed gun club' and sparking up a conversation about it in front of others.
I should add that the motivation may be good natured, with a friendly intent, but its immature to tell others about someone else's private information just because you discover or think you have discovered it. Unless you think they pose a risk or potential risk and are telling someone else to keep an eye out, bringing attention to a responsible individual carrying in a way that is clearly intended to be private and is unknown to others around is bad manners.