The system where the object is placed decides its weight. The weight of an object may vary with the location since weight is a force and you need to remember that force is the product of mass and acceleration. The value of acceleration measured on Earth is not the same with the value of acceleration measured on space. Since weight force is gravity, the acceleration is about 9.8m*s^(-2), hence if the mass of an object is of 1 Kg, then the weight is about 9.8 Newtons (remember that standard unit of measure for force is Newton).
You should remember that the mass remains constant unless you change the material and dimensions the object is made of since mass expresses the relation between density of material and volume of object.
Hence, only mass should be expressed in Kilograms. Though, weight is expressed in kilograms to avoid confusion created by the Newton unit of measure that implies a multiplication of number of mass by the acceleration value `9.8 m*s^(-2).`