The weapon you see on the screen is a effect, but has not *direct* relation to the origin of the shot. On some weapons the origin could be the center of the body mass, or somewhere "on the right", but not where you see the weapon. You can display a ray from the origin where some weapon will be shot, and where it will hit, but thats could result on a surprising experiments as the ray can be different to what you expect, and much probably not connected in any way with the weapon you have in hand.
It could be most weapons seems shot with a "Shoulder cannon", like in the Predator movie.