Say you had two coins, one was larger (twice the size) of the smaller coin.
Since the smaller coin was half the size, logically you would be able to store at least twice as many in the box. But since the spacing between smaller coins is less than larger coins (ie, less wasted space tesselating them), would you be able to store more than double?
Yes.
Proof:
Given a box of side length 1cm, you can fit zero coins of diameter 1.2cm but can fit at least one of the smaller coins at half the diameter (0.6cm).