It’s true that speeding an object up to considerable fractions of the speed of light will make things behave like they are more massive than they do when they’re moving at slower, more human, speeds. But going the other direction is not as easy. Objects which are not moving at relativistic speeds are measured to have what’s formally known as their rest mass, the mass that you get when you sum up the masses of all the individual particles that make them up. For a human, this rest mass usually puts people at a mass of tens of kilograms (between 50 and 80 kilograms is 110-175 pounds).
It’s relatively easy to make something weigh less, as weight is the interaction between a mass and the gravitational field of the Earth. Want to make something weigh less? Try putting it in a gravitational field that isn’t as strong. The Moon is a good place for this kind of experiment; with a gravitational field only a sixth as strong as the Earth, a 60 kilogram person would feel about as heavy as a 10 kilogram baby (a milestone the median girl hits at 13 months old, and the median boy hits at 11 months).
There’s also weightlessness, which we can experience on Earth in amusement park rides which drop you from a height, specialized planes like the Vomit Comet, or if you’ve gone skydiving. All of these situations have something in common; you’re falling. Technically speaking, the sensation of weight is provided by a contact between your body and something else - for us humans, this is typically the floor, a bed, or a chair. If you’re falling freely, that contact is missing, and you can feel like you weigh nothing. The astronauts in the International Space Station get this sensation for longer periods of time, but the ISS can be thought of as very carefully perpetually falling. (The sideways speed of the ISS allows it to fall around the planet instead of down towards the surface.)
However, in all these weight-altering situations, the mass of our people or objects would still fundamentally remain the same as it was when they were sitting, on their own, on the surface of our planet. Measurements would bear that out no matter how paltry the gravitational field of the world you’re standing on, or how much you happened to be falling at the time. These are all completely expected behaviors of a massive object, given a particular motion within a particular gravitational field.
Can you make something behave like it has less mass? Not unless you remove some material from the object. There are lots of ways to remove mass from an object, but most of them involve physically removing some of the object. You can remove mass either mechanically, by making the object physically smaller, or made of different materials, or by converting some of the mass into energy. Converting mass into energy is not an easy thing to do (which I find very fortunate, as I personally like being stable as an entity of matter and not an unstable energy bomb) but it can happen in the Universe. The most dramatic recent example is that of the binary, merging black holes detected by LIGO - the final black hole is considerably less massive than the sum of the two black holes - the remaining mass was lost, converted into the energy required to produce the gravitational waves in the first place.
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