How do we know the size of atoms in body centered cubic system?
The easiest answer in my opinion; try it! If each atom has the same radius, it is simply not possible to fit one of them into the center of the cubic system (known as a cubic hole). It is, however, possible if the atom is sufficiently small. CsCl is an example of such a compound. 

One can show this geometrically (as is done here), but you can also convince yourself that it must be the case using equally-sized tennis balls or something similar to try it out in practise.