As a retired Corporal I can assure everybody, that running with a 2.50 lb pistol in one hand, while having the other one free is extremly irritating because of the imbalance - and therefore as *cumbersome* as running with an 8.0 lb rifle in both hands.
And even if the hands are free, the whole equipment - including weapons - has to be tightly strapped onto the body to gain a little speed. Metal Devil is right of course, the weight is always there
If you want to add little more realism for different weapon types, it can be added when using ironsights:
It's not that a soldier is actually slower while aiming with a heavier weapon. But since the weight of the weapon on the supporting arm is a factor, he
has to move slower to keep a steady aim.
Regarding the airmode settings that allready exist, to my experience, the speed for pistols is a little too slow when using ironsights. A larger speed gap between pistols, submachingeuns and assault rifles would be more realistic. Also turning around while aiming with a pistol is nowhere as cumbersome as with a rifle because the momentum resulting from the weapons weight has to be taken into account. For the only project I used airmod settings so far, I drastically increased the turning speed for pistols.
In case you find my grammar and spelling weird ---> native German speaker ^^