Originally Posted by Gingervytes
Because that's not an analogous system.
Newtonian mechanics defines its terms precisely. A "particle" is that upon which elementary forces act, and which exhibits unary reactions. A "system" is a collection of particles related by mechanics described in the laws of motion and other physical laws. We may reckon some of the physical phenomena of mechanics in terms of net effects, summed across the system. We can also describe different values for those same properties confined to their behavior within the system. Until you understand this, you cannot properly reason your way through Newtonian problems.
A mass on a scale in a gravity field describes a system composed of the mass, the scale, and the Earth. When you lift the weight off the scale, you have introduced a force that is external to the system. There is no expectation that momentum will be conserved in that frame of reference. In a different frame of reference, the weight, the scale, the Earth, and you comprise a larger system. If you lift the weight off the scale, the net momentum of that system remains the same despite the velocity and position information of particles in that system having changed. There is no expectation that momentum will be conserved among all particles in a portion of the system. That is, how you specify the system is of utmost importance.