“Hanging down off you from every point” is the complete opposite of “distributed across your entire body,” so I haven’t explained myself clearly.

For me, wearing chainmail was like having literal chains hanging off me, all down my arms, my shoulders, my head (I was wearing a chain coif), my hips, my legs, pulling all the way down to the ground. Moving around felt like trying to walk underwater, or what I imagine it would be like to walk on a planet with heavier gravity.

By contrast, when you’re wearing plate armor, it doesn’t feel nearly as heavy because a lot of that weight is getting spread sideways instead of hanging straight down, so you’re carrying more of it across bigger muscles like your back and it’s not fighting your movements nearly as much. It’s not weightless, but it’s something that’s been designed to allow you to move as freely as possible while still being protected as much as possible.
Think of it as the difference between carrying a whole bunch of weights loose in a sack versus those same weights that have been carefully packed into a fancy frame backpack so that the weight’s distributed really evenly.