How do I change the weapons of the other characters I hang out with?

Sadly, there is no way to make them change the weapon that they are using.

Internally, the game decides what is the best weapon for the other characters (being considered pedestrians when not controlled), so for some reason the game decided that the Gusenberg Sweeper was the best weapon for them.

If you still want to change the weapon, your only option would be to get rid of all of the weapons that you don't plan to use.