What does "weapons are easier to handle" mean?

"Easier to handle" means that guns do not have as much muzzle climb, so your aim does not stray upwards under sustained fire. The bullet spread DOES increase normally as you shoot however, your aim just says where you put it so there's no need to compensate for recoil.

To test this, stand still and fire an Assault Rifle for a second on casual mode and then on normal mode. Your aim will remain the same after 1 second in casual mode, but you'll be looking up in normal mode.

This does not appear to affect clip size, reloading, accuracy, bullet spread or auto-aim at all. There seems to be only one "level" of easier weapons, there's no difference in handling from Normal to Insanity, and Casual and Narrative mode appear to have the same lack of muzzle climb.