Material quantity has to do with how much of something there is in a given place. Colloquially, it is measured using pounds or kilograms, but many scientists prefer mass, which more objectively describes the material quantity in a given sample. Because mass is usually correlated to weight in everyday situations, kilograms are also used to measure mass.
When chemists refer to the material quantity of particles in a sample, they often use moles, a quantity that refers to roughly 6 x 1023 units of something, usually atoms or molecules. The large number is known as Avogadro's number or Avogodro's constant, named after the Italian scientist Amedeo Avogadro, who realized, in the early nineteenth century, that the volume of a gas is proportional to the material quantity of particles within the gas. Avogodro's number is defined as the number of atoms in exactly 12 grams of carbon.
As long as a system does not lose or gain atoms, either though exchange with the outside or nuclear fission/fusion, it retains the same amount of material quantity indefinitely. There is the possibility that protons, which make up the nucleus of atoms, spontaneously decay after an extraordinarily long length of time, but this has not been proven and there is little evidence in its favor.
The same material quantity may have a different weight depending on what planet it is near. For instance, on Jupiter, you would have a weight dozens of times greater than on Earth, so extreme that it would break your spine. Conversely, on the surface of the Moon, gravity is roughly 1/4 that of the Earth's, so your weight is about 1/4, even though your mass (and the material quantity of particles in your body) stays the same.
Another instance where material quantity can be constant while weight fluctuates is when something is moving very close to the speed of light. According to Einstein's theory of relativity, when something moves extremely fast, approaching the speed of light, it gains weight. This is why a particle with nonzero mass can never move at the speed of light — as its velocity increases, so does its mass, thereby making it more difficult to accelerate. The energy requirements to continue acceleration to the speed of light are infinite — greater than the total amount of energy in the universe.