a lot of the weight would be distributed down to the rest of the armour and padding the helmet rested on and thus the shoulders took a lot of the burden. i think they and the rest of the armour were heavier as manning the walls didn't require the same mobility as on a battle field, and the extra thickness helped against missiles. if the enemy ever got over the walls and fighting became hand to hand, a lighter armour might be better. you could switch if you knew when they were going to make it over.
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