Question

where on earth will the weight be zero

Answer 1

as gravity is null in centre of earth .weight will be zero at the centre of earth

Answer 2

Yes weight can be zero. Consider yourself…

Let your “mass” be ‘m’ kg (Note that mass of an object can never be zero… atleast for large object i.e. non- nuclear and electromagnetic particles.)

Let W be your weight.

Hence your weight is… W=m×g Newtons

Here, g is the acceleration due to gravity which is constant for a place. In places where g is zero (like outer space) or where you are in continuous free fall (like ISS, but this condition is not fully weightless, hence it is called microgravity) or when your body's weight is balanced by some other external force (Your weight is the force exerted by your mass on earth) your weight can be zero.

That is, if the total/resultant 'g' is zero, W=0.