As a runner, I also wondered about this. So I got an Apple, bound it to my ankle with an Ace bandage, and tried jogging. I didn't try with it on the inside, but on the outside (where it should be), and there was NO impact on my movement.
That said, I don't know how much an ankle bracelet weighs. Given how lightweight our everyday GPS items are, like fitbits and phones, can't imagine that they need to be too heavy.
Perhaps if FD's issue is running comfort, he should request a TIGHTER ankle band that stays in place!