There are many metric systems not just one and they have changed over time. The commonly used all over the world is the SI (International System of Units) the abbreviation is from the french name (Système international d’unités)
> But grams are a measurement of weight,
No, it is not. The SI unit of weight is Newton, weight is a force so you use the unit of force. It is not uncommon that people say wight when the mean mass,
Historically kilogram-force, also called kilopond m has been used as a metric unit of force. That is the force of gravity on a mass of 1 kg on the standard gravity on earth.
It was never part of the SI system used today. SI was created in 1960 and Newton as a force was accepted in 1948.
It is not uncommon that people say wight when the mean mass, or use kilogram as it was used historically, but it is not a part of the SI system
US customary unit pound-force for a force and pound-mass for mass, often just calling them pound
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