If weight is measured as M * g (mass x gravity), then how does the "weight" of a massive helium filled balloon negative? Let's say you have a 63,000 m^3 helium balloon. The mass of the helium is around 11,000 kg! 11,000 kg * 9.81 is a substantial amount of "weight", but the measured weight is negative due to the density differential with the surrounding body of fluid (air). What accounts for this mathematically? Is the "g" term negative? Is the m*g weight equation not valid in this case?
Most objects have densities that are very much larger than that of air. For calculating the motion of these objects in air, the buoyancy force can be neglected without introducing substantial errors. If you define “weight” as what a scale reads, though, it is technically not exactly $w=mg$ unless the object is in a vacuum, but rather $w=mg-\rho g V$, where$V$ is the volume of the object and $\rho$ is the density of the surrounding fluid. For a helium ballon, this second term (the buoyancy force) is not only not negligible, it is larger than the gravity force. So $w$ is negative.
the helium balloon is experiencing a force in addition to that of gravity which you have not taken into account: the buoyant force caused by its being immersed in a medium that is more dense than it is.