Carat weight is not a factor which denotes diamond quality. It purely denotes the size of a diamond, by its weight. Obviously it also affects the value or price of a diamond, because consumers tend to prefer bigger rather than smaller diamonds.
Large diamonds are also rarer than small diamonds.
Because there is higher demand and lower supply for large diamonds, they command higher prices. Often people talk about the size of diamonds. Size in this context really means weight, as large diamonds will normally weigh more than small ones. Historically the carat is supposed to have been derived from the weight of locust bean or carob bean seeds, from the Greek Keraton. Until earlier this century, there were at least two different standards for the carat.