ctw = Carat Total Weight
When a price tag or appraisal uses the abbreviation “ctw”, this refers to the total weight of all the gemstones in that piece. For instance, a ring might be stated to contain 0.50 ctw diamonds, and 2.00 ctw emeralds. This just means there are 1/2 carat total when you add up the weight of all the diamonds in the ring, and it has a total of 2 carats of emeralds when you add the weight of all the emeralds.
Be careful not to think that the ring has ONE diamond of 1/2 carat in weight — when it only says 1/2 ctw, or 0.50 ctw — which is very very different in value. Smaller diamonds are priced a lot less per carat.