Because the hopping integrals changes for the exchanged electrons. It is easy to understand that the probability of going from one state to another in a different atom depends of the number of available ones. Isn't?

I thing Dr. Daniel answers  the question briefly.  However, one may also understand that if you change the number of atoms say from N to N+1, you adding N more terms to net binding energy of the complex.  Naturally the binding energy is bound to depend on number of atoms in the complex.