Precision machining to get items that can be perfectly balanced is not an easy task. You can have a computer-guided CNC machine make a product to exacting measurements then anomalies in the structure of the materials it is made from can affect the balance. This is why high quality veterinary scales are needed for what we do. We need to make items that can balance on a fine point that will remain motionless not leaning to one side or the other. We use a balancing scale to fine tune each part.
We make items that balance on the head of a pin so perfectly that even a truck going by can make them move. In the lab we have a scale called a laboratory balance that tells us with precision how much material needs to be removed on either side to bring the object into perfect balance. Ours even has draft shields so movements of air current stirred up by lab workers moving about or the air control system do not affect balance. It is very highly detailed precision work.
Each piece needs to be hand adjusted to perfect balance. Think of the rims on your car for example. You will find wheel weights even on a brand new car. You might think that the manufacturing process would produce exact copies of a perfectly balanced wheel, but that is not the case. Each new one needs to be hand balanced. Not only are the wheels not made perfectly, but the tires on them cause balancing issues too. That is why they need rebalanced every time you get new tires. Our laboratory balance does pretty much the same thing just on a smaller scale with smaller parts. The scale allows us to make precision testing equipment for our experiments that has unparallelled accuracy.