A US $100 bill weighs about 1 gram.
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A $1000 bill weighs about 1 gram, the same weight as any other US currency bill.
All U.S. notes weigh about 1 gm regardless of denomination. Also, this site has a Coins and Currency thread that is more appropriate to questions about, uh, coins and currency. Miscellaneous questions tend to be ignored as leftovers.
A trillion dollars in one hundred dollar bills would weigh about 11 million pounds, or roughly 5,000 metric tons. The weight of the bills comes from the density of paper currency, which is approximately 1 gram per bill.
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A standard piece of notebook paper weighs about 4.5 grams.