With regards to jewelry: Carat weight is most often used when weighing precious or semi precious gemstones (from diamonds through amethyst and really good lapis for example); Gram mode is the choice for most semi precious gemstone cabochons and rough, as well as the amount of precious metal in an object (such as a finished diamond ring that is made using 5 grams of 18kt gold and labeled for sale as such); Pennyweight can be used for the weight of any metal from gold through ready-made construction nails! (The term "pennyweight" comes to the world from England and has an interesting origin, as I found in this brief article,
Pennyweight.)
Here's another bit of information: when spelling, Karat is used with relation to the purity of metals, and Carat it refers to gemstone weight.
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Answer contributed by Dale "Cougar" Armstrong