Is two different sizes of diamonds with equal weight cost same?

No.

Every raw, natural diamond is chemically different from every other diamond, because Mother Nature's crafting systems are not standardized.

Every diamond gemstone is valued by its cut, clarity and colour in addition to its carat weight. For example, today on Blue Nile you can purchase a 1.02 carat diamond, round brilliant, I colour, SI2 clarity and pay US$3,499. As well, you can purchase a diamond of exactly the same carat weight, marquis cut, D colour, Flawless clarity, and pay US$17,129.