It's probably better to think about the other way around. Despite heroic efforts, the "old" kilogram was getting (a tiny big) lighter every time it was handled

It's probably better to think about the other way around. Despite heroic efforts, the "old" kilogram was getting (a tiny big) lighter every time it was handled. The "new" kilogram will finally be a constant. To a reasonable approximation it hasn't changed at all at this moment time.