It appears to me that you are confusing "mass" with "weight". Weight is defined as "the force with which a body (or mass) is attracted towards the center of the earth". So, Newton as its SI unit is absolutely normal and it cannot be anytthing else.
A mass of 'M' Kilogram is attracted to the center of the earth with a force eaual to M*g Newtons. Mg Newtons is also defined as M Kilogram weight. So, "Kilogram weight" is another unit of Weight --- but, it is not the SI unit.