You make a point that I studiously avoided! Yes, MASS stays the same under any acceleration, but WEIGHT varies with the local 'g'. In orbit, free-fall (or while falling off the Burj Khalifa - 18 seconds!) your weight is zero. When you hit the ground, it's another story.
John
PS You don't "Weigh" any number of newtons - it's a force, not a mass.
PPS It's also an SI unit, and is therefore, like ohms, pascals, joules, watts, teslas, henrys, bequerels, seiverts, grays, etc, etc, spelt without a capital letter. Except for Celcius! Because they are degrees OF Celcius!