The price per carat does not increase smoothly with increasing size.
To keep it simple for D&D I am keeping the weight of all gems the same and only vary the value depending on gemstone type and size. The density of gems varies from very light stones like opal to especially heavy stones like sphalerite or zircon.
In the real world, gem sizes do not determine weight. The information listed here is provided for those rare occasions when your character may need to carry an exceptionally large gem or a very large number of gems. Unless your character is carrying an extremely large number of gems, their weight is insignificant and you do not have to keep track of it. They are carried in small leather or cloth bags tied securely with a string or leather strap.
Standard gems carried by adventurers are 1/4″ in diameter. I started with the official D&D information and expanded on it. Here is some information regarding D&D gems.