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It is not the weight, it is the fineness/ purity of the gold alters the carat weight. This id done by fractioning and precentages; we all know 24ct is the 100% pure gold.So 9ct is 9/24th's of 100% gold, which equals 37.5%. Hence why the hallmarking is given as parts per thousand of gold ( 9ct = 375)

9ct = hallmark 375 = 37.5% gold, 62.5% base metals/alloy

18ct = hallmark 750 = 75% gold, 25% base metals/alloy

22ct = hallmark 916 = 91.6% gold, 8.4% base metals/alloy

24ct = hallmark 990 = 99.0% gold which is the minimum for it to be classed as pure.

Gold is mixed with alloys to make it stronger, durable and less malleable, retaining its shape when cast. Therefore 9ct and 18ct is a preferred choice.

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What are the percentages of gold in the different karat weights of gold jewelry?

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Is k an identifying mark on precious metal jewelry?

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