Distillation: Simple vs Fractional
So, why does simple distillation put emphasis on small amounts and
  fractional distillation, on large volumes?


It's not small and large volumes of material being distilled, but rather small and large volumes of impurities present in the material to be distilled.  Both simple and fractional distillations can be used to distill large quantities of material.  

The efficiency of a distillation column is measured in "height-equivalent theoretical plates" (HETP), the more plates the more efficient the column, the more efficient the column the more likely that it will be able to separate two closely boiling materials.  If you have a small amount of a lower boiling impurity in your solution and you want to separate it from a large amount of the desired material, then you can probably get away with using a simple distillation column and discarding some of the forerun (the first drops of liquid that distill over).  On the other hand, if there is a large amount of impurity and it boils close to the desired product, then you will need a column with a higher efficiency (fractional distillation column) to effect a good separation between the two fractions (or "cuts" as they're sometimes called) and get pure product.

To sum up, perhaps the original question would be better written as


  So, why does simple distillation put emphasis on small amounts and
  fractional distillation, on large amounts of impurities?


and the answer would be that even an inefficient (fewer HETP) simple distillation column has enough power (enough theoretical plates) to separate a small amount of impurity from a large amount of product, especially if you are willing to discard the initial fore-run from the distillation.  If there is a larger amount of impurity, then we may need a more powerful (higher efficiency column) to produce the desired separation.  

The higher the efficiency of a distillation column, the greater its ability to separate two things.  If we have to separate two materials that are both present in large quantity, or distill at boiling points close together, then we need a more efficient column than if they boiled further apart or one was present in only a small amount and we were willing to throw away the forerun (e.g. throw away some of the desired product in that early fraction that contained the impurity).  When we call a column a fractionation column, we're really saying that it has greater separating efficiency than a simple distillation column.  The more efficient the column, the better the job it will do on difficult separations.