Any two bodies with a mass are attracted towards each other by a force directly proportional to the product of their individual mass and inversely proportional to the square of the distance separating them.
The exact force with which two bodies with mass M1 and M2 and separated by a distance R is given by F = G*M1*M2/R^2 where G is the gravitational constant and equal to 6.674*10^-11 N*m^2/kg^2.
The weight of an object on any other object refers to the gravitational force of attraction between the two. This is expressed in terms of Newton. Mass on the other hand is expressed in terms of kilograms. For example an object with a mass of 1 kg has a weight of 9.8 N on the surface of the Earth. If the object were placed on another planet its mass would continue to remain the same while its weight would vary with the mass of the planet and its radius.