  We extend the systematic calculation of an approximately relativistic
Hamiltonian for centre of mass and internal dynamics of an electromagnetically
bound two-particle system by Sonnleitner and Barnett [1] to the case including
a weak post-Newtonian gravitational background field, described by the
Eddington--Robertson parametrised post-Newtonian metric. Starting from a proper
relativistic description of the situation, this approach allows to
systematically derive the coupling of the model system to gravity, instead of
`guessing' it by means of classical notions of relativistic effects.
  We embed this technical result into a critical discussion concerning the
problem of implementing and interpreting general couplings to the gravitational
field and the connected problem of how to properly address the question
concerning the validity of the Equivalence Principle in Quantum Mechanics.
