What is your weight in newtons if your potential energy is equal to 1000 joules and your mass is 60 kg

Your potential energy and mass don't tell what your weight is.

If I walk up from the first floor to the second floor, my weight hasn't

changed even though my potential energy has increased.

Weight force is equal to mass times the acceleration of gravity. Since we're close on earth gravity is about 9.8 m/s^2. Multiply 9.8 by 60 and you will get 588 N. The potential emergy doesn't really matter here (unless you were on a different planet with different acceleration of gravity and given a height about the ground).