The appropriate unit to measure weight is the newton. Now, if it is really the mass you wanted, you could use kilogram or gram.
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Grams is no good - it is a measure of weight not length. Kilometers measure length - but only if your table-top is a few miles long. Most appropriate would be Meters - your average dining table is about one-and-a-half meters long.
What is the most appropriate instrument to measure
inches
kilograms
a centimeter