The weight of $1 billion depends on the denominations that were used. If the currency were strictly in $100 bills, $1 billion would weigh roughly 10 tons. If one is using $1 bills, $1 billion would weigh 1,000 tons, which is equal to 2 million pounds.
Additionally, $1 million weighs roughly 22 pounds in $100 bills. Similarly, if that amount of money were only in $1 bills, that $1 million would weigh a little over a ton. A person with 10 billion $1 bills who spent one every second of every day would take 319 years before running out of money.