Question

if weight is the force of gravity on an object, then your weight can change if the force of gravity is different on a different planet?

Answer 1

Yes, your weight can change if the force of gravity is different on a different planet.

Like on the Moon because acceleration due to gravity is 1/6 that on the Earth, your weight on the Moon would be 1/6 the value on the Earth.
 
But note that you mass remains the same.