At this point, it is important to remember that science concerns itself with the observable, and that we can only observe objects by letting it interact with external forces, and an act of observance is accompanied by some sort of disturbance of the observed object.
We can then define an object to be big when the act of observation carries with it a disturbance that is negligible, and small when the disturbance is non-negligible.
We assume that by being careful, we can minimize the extent of the disturbance as much as we'd like: the concepts of big and small are thus relative, and really refer to the degree to which our observation creates a disturbance in the observed object.
In order to give an absolute definition of size for a fundamental theory of matter, we have to assume then that there is a limit to how finely we can make observations, and how negligible the subsequent disturbance can be.
A limit which is inherent in the nature of things and can never be surpassed by improved technique or increased skill on the part of the observer.
If the observed object is not affected by the limiting disturbance, it is big, and we can consider it classically, however if the disturbance is not negligible, then we require a new theory for dealing with it.