Weapon weight should definitely change the characters/players mechanics. You shouldnt be able to run at full speed when carrying a RPG as opposed to a pistol.
A RPG-7 Developed by Russia weighs in at 17.42 lbs (7.90kg) witha range of 328 yards (300m)
A 1911 currently weighs in at roughly 2.4 lbs (1.08 kg)
Sure, not every one will want the physics changed based on the weight of their weapons of choice and I can see making it a simple booleen function or something similar. I personally think its better to have the weighted physics as it adds another level to the game. Think of it as on the same level of only being able to carry 2 weapons at one time and being able to pick up another in exchange for the one in your hand. More gear = more weight. More weight = slowing down. Not all of us are as strong as atlas.
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