  The notion of `weak classical limit' for coupled N-level quantum systems as N
-> infinity is introduced to understand the precise sense in which one attains
classicality. There exist proofs that a system becomes classical at large N. On
the other hand, it is known that non-locality and entanglement, the two
hallmarks of non-classicality, thrive even as N -> infinity. We reconcile these
results in this paper by showing that so called classicality is not so much an
inherent property of the system, as it is a consequence of limited experimental
resources. Our focus is largely on non-locality, for which we study the
Bell-CHSH and CGLMP inequalities for N-level systems.
