How to quickly identify who carries which weapon?

Outdated, now you can see that quickly when assigning a weapon to a Dweller. See other answer.

_{I still like my redhead squad, though.}

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You cannot.

The only gun carriers you can quickly identify are those guarding the gate, since they have their weapons drawn.

The game gives you no quick way to identify all weapon carriers, so you will have to be organized.

You could, for example :

• Give weapons only when needed, then take them back (as suggested in on of the comments)

• Have your "defense squad" stationed in one particular area of your vault

• Give the weapon only to certain people : people with military suits (so RP !), women with red hair…

Since the update awhile ago, this has actually become quite simple. When selecting a weapon for a dweller, the default list has the leftmost column labeled "Inventory", and shows all unequipped weapons. If you tap that, it will change to "Equipped", showing all weapons currently equipped along with who carries them. Tapping again gets you "All", which contains all equipped and unequipped weapons.