I would think it would drag you backwards as there’s more of it behind than in front, especially as it moved, and could potentially pull at your neck as well. If you could keep it well balanced over your shoulders you might be okay, I suppose.
You’d have to figure out a way to keep it in front of you. A cloak will swing behind you when you move. It’s designed to do that, so that it frees your arms to do other things. It’s basically a long coat without sleeves, and without sleeves it has to get out of the way for you to do anything with your arms or hands.
The point of this scheme is so that if someone attacks you, you can swing the cloak to deflect the attack, and even swing the cloak at someone to injure them. That requires the weight to be distributed toward the hem, not the shoulders.
I remember the argument in the community we belonged to (an online text-based role-playing game) and no amount of logic would dissuade the guy.
I know I’m sold, which is a relief. It’s a pain carrying this harpoon around.
But at least it’ll quench your thirst
Depends. Do you have a towel?
A big magnet.
Check. Mate.
…That attracts zinc?
Precisely.
Then checkmate indeed.
I don’t know why someone would line a cloak with pennies as a weapon; I mean, personally, I’d use dimes; which would be better! If my arithmatic calculations are correct, it would be 10x better. 
I was picturing a cloak with sharpened pennies sewn in the lining just at the hem. Like the apocryphal flat caps of the Peaky Blinders gang, only pennies not razor blades.
Not that copper holds an edge, mind you.
That’s why we use zinc in pennies. Genius!
Not if you fall into water, because then you’ll zinc.
Go to your room.