Sorry, my bad:
Old:
New:
The idea is that when you run with a gun or without, you counterbalance your body with the swaying of your arms, so when right leg goes forward, right arm goes back, and when you carry a weapon the same idea apply, except you use your gun to keep the balance.
I think you do not really notice until someone point it out, it is an easy thing to overlook in a game you have always loved :)