The Roosevelt dimes that you find in your change weigh 2.268 grams or 0.080 ounces. These modern day Roosevelt dimes have been minted since 1965 and they consist of 91.67% copper and 8.33% nickel.
Before 1965 the US government issued silver dimes and they weigh slightly more than the current dimes. The silver Roosevelt dimes, Mercury dimes, and Barber dimes all weigh 2.5 grams, an increase of 0.232 grams.
In addition, there were older US dimes minted in the late 18th century and 19th century. The first ever dime was called the "Disme". It was minted in 1792 with a weight of 2.7 grams. The Draped Bust dimes and Capped Bust dimes followed and they had the same weight of 2.7 grams. The next series was the Seated Liberty dime and it went through design and weight changes over the years. It was first minted in 1837 with a weight of 2.7 grams. In 1853 the new issues came out with a weight of 2.5 grams.
See also:
How Much Does a Penny Weigh?
How Much Does a Nickel Weigh?
How Much Does a Quarter Weigh?