重さ and 量: weight and amount
Distinguish weight as a measurement basis from amount more generally, and track changes separately from totals.
Stating weight
重さ, read おもさ, means weight. 荷物の重さは三キロです。 says that the luggage weighs three kilograms.
重さが同じでも、大きさは違います。 says that the weights match but the sizes differ. Equal weight does not mean equal size.
Stating amount
量, read りょう, means amount or quantity. 水の量を減らしました。 means reducing the amount of water.
仕事の量が増えました。 says that the amount of work increased. 量 is not limited to substances that can be weighed.
Measurement basis and change
砂糖の量を重さで確かめました。 means checking the amount of sugar by weight. Weight is the basis used to establish how much sugar is involved.
量を半分にしましたが、全部はなくしていません。 says that the amount was halved but not eliminated entirely. Distinguish reduction from complete removal.
Does 仕事の量が増えました mean work was measured in kilograms?
Show the answer and why
No. It means that the amount of work to be done increased.