  The large nucleon-nucleon scattering length, and the isospin approximate
symmetry, are low energy properties of quantum chromodynamics (QCD). These
entail correlations in the binding energies of light nuclei, e.g., the A=3
iso-multiplet, and Tjon's correlation between the binding energy of three and
four body nuclei. Using a new representation of these, we establish that they
translate into a correlation between different short-range contributions to
three body forces in chiral effective field theory of low-energy nuclear
physics. We demonstrate that these correlations should be taken into account in
order to avoid fine-tuning in the calibration of three body forces. We relate
this to the role of correlations in uncertainty quantification of
non-renormalizable effective field theories of the nuclear regime. In addition,
we show that correlations can be useful in assessing the importance of forces
induced by renormalization group (RG) transformations. We give numerical
evidence that such RG transformations can be represented effectively by adding
a constant to the pure three nucleon contact low energy constant $c_E$.
