If a recipe asks for 50g of confectioners sugar, what is the weight required in caster sugar. I am making a no bake cheesecake
In general in recipes measuring by weight, you can use the same weight, as 50g of one kind of thing is usually the same amount as 50g of another kind of the same thing (in this case sugar). With volume measurements this is not the case, as certain kinds of things will pack into the measuring cup differently (flour is notorious for packing, for instance, and no two cups ever seem to come out the same).
In your specific case, however, a direct substitution may mot work as desired. Confectioners or powdered sugar often has a small amount of cornstarch mixed with the sugar to prevent clumping. Its possible that a no-bake style cheesecake recipe may be relying on that, so you may want to substitute a few grams of cornstarch for some of your caster sugar. I would try 45g sugar and 5g cornstarch.