Are body weight and weight the same when measured at mid-latitudes and at the Pole?

1. In classical mechanics, body mass is one of its fundamental properties, and does not depend on anything, so the body mass will be the same.
2. The weight of the body is the force with which the body acts on the support P = mg. At mid-latitudes, the acceleration of gravity (g) will be different, because the Earth is flattened at the poles, then the radius at the pole and at mid-latitudes will be different: g = GMz / Rz ^ 2. Thus, the radius at the pole is less than at mid-latitudes, which means that the acceleration of gravity at the pole is greater than at mid-latitudes, as a result, the weight of one and the same body at the pole is greater than at mid-latitudes.