Ah ha ! Very interesting question. Thought-provoking, even.
You have something that weighs 1 Newton, and you want to know the situation in which the object would have the greatest mass.
Weight = (mass) x (local gravity)
Mass = (weight) / (local gravity)
Mass = (1 Newton) / (local gravity)
"Local gravity" is the denominator of the fraction, so the fraction has its greatest value when 'local gravity' is smallest. This is the clue that gives it away.
If somebody offers you 1 chunk of gold that weighs 1 Newton, you say to him:
"Fine ! Great ! Golly gee, that's sure generous of you. But before you start weighing the chunk to give me, I want you to take your gold and your scale to Pluto, and weigh my chunk there. And if you don't mind, be quick about it."
The local acceleration of gravity on Pluto is 0.62 m/s² , but on Earth, it's 9.81 m/s.
So if he weighs 1 Newton of gold for you on Pluto, its mass will be 1.613 kilograms, and it'll weigh 15.82 Newtons here on Earth.
That's almost 3.6 pounds of gold, worth over $57,000 !
It would be even better if you could convince him to weigh it on Halley's Comet, or on any asteroid. Wherever he's willing to go that has the smallest gravity. That's the place where the largest mass weighs 1 Newton.
