Why has nobody create negative gym weights? By that I mean weights which take away from the overall weight you're lifting instead of adding to it.

Say you wish to squat 200 lbs. The barbell weighs 45 lbs so you need to distribute 200 - 45 = 155 lbs equally on both ends of the barbell, resulting in 77.5 lbs on each side.

In a traditional gym, that will take a 45 lbs plate, a 25 lbs plate, a 5 lbs plate, and a 2.5 lbs plate. That's a total of four plates on each side. It would be easier if you could use a 45 lbs plate plus a 35 lbs plate, which add up to 80 lbs, and then subtract 2.5 lbs using a negative weight. That's only three plates.

I suggest negative weights be made of a very light shell and filled with a gas that's lighter than air (more on that below). A negative weight of 2.5 lbs would pull the barbell slightly upward, in the opposite direction of gravity, thereby resulting in a lift that's 2.5 lbs lighter, saving you a plate.

Negative weights would also help you reduce the weight gradually without having to replace plates. Say you're squatting at your maximum weight, one rep per set. You start with one rep at 200 lbs. For your next set, you want to do one rep at 180 lbs, which is 67.5 lbs each side of the barbell. That's 45 + 10 + 10 + 2.5. You need to transition to that from having, on your barbell, 45 + 25 + 5 + 2.5. That means you need to take off 2.5 and replace both the 25 plate and the 5 plate with 10 each, only to put the 2.5 plate back on again. That's a mess. It would be much easier if you could simply keep those weights and add -10 lbs on each side. Maybe you have the foresight to stack your plates in such a way that reducing the weight is easier – but some days you feel stronger than others, and you may have to reduce weights unexpectedly. And math is easier the less you need to do of it, especially when you're out of breath.

In the same vein, negative weights would make transitioning to other, lighter-weight exercises easier. They could also help you with assisted exercises, such as assisted pull ups, where they could be mounted to your body somehow, pulling you up slightly. Conversely, when you're working with gravity, negative weights could make your exercise more challenging.

I suppose a downside of negative weights is that when they're not properly secured they end up floating around the gym ceiling. And you shouldn't take them outside. But surely this problem is soluble.

Which gas to use? It appears helium wouldn't work very well because you needs lots of it to lift even very light weights. For example, you need the volume of 33 balloons to lift even one pound. But maybe that can be fixed somehow. Or maybe there's another gas of which smaller amounts are required to lift objects. Or the weights could have little thrusters. Something. Somebody please create negative weights. (And then a universal dumbbell that you type the desired weight into and it magically weighs that much.)