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They are used mainly to weigh things, and occasionally to build muscle.
weights are not required for pilates, as it uses the weight of the body and gravity for resistance. The key is to build suppleness and strength in a non strenuous way.
ammunition paint (in the old days) food cans fishing weights..
The only difference between a Bowflex machine and free weights are wires. The Bowflex machine uses weight resisting wires to increase your weight. With free weights you are using your own muscle to rely on.
I use maths in the kitchen to calculate cooking times and the weights and measures of ingredients.
The most important use of lead is in batteries. It is also used as weights. Ballast in sailing ships, diving weights, car tyre balancing weights. Also it is used as a component of some metal alloys. The most familiar of these is solder. Lead is used in making pigments (though now it is banned in a lot of uses due to health concerns).
If you are referring the the US Standards of numbers, weights and measurements, I believe that We are the only ones. Most of the rest of the World uses the Metric System.
India, along with 96% of the world, uses the metric system. Weights are therefore measured in grams.
By doing shrugs, with or without weights, one uses many muscles. Shrugging uses the teres minor, supraspinatus, infraspinatus, subscapularis, the delta and traps.
Go free weights all the way. Machines give ease of use, but free weights are a much harder workout. With free weights, you have to control the balance of the weight and keep a good even movement, which uses muscles that would not be used normally with a preset machine.
India officially uses the metric system of weights and measures, like all countries except the U.S.