  The quark mass dependences of light element binding energies and nuclear
scattering lengths are derived using chiral perturbation theory in combination
with non-perturbative methods. In particular, we present new, improved values
for the quark mass dependence of meson resonances that enter the nuclear force.
A detailed analysis of the theoretical uncertainties arising in this
determination is presented. As an application we derive from a comparison of
observed and calculated primordial deuterium and helium abundances a stringent
limit on the variation of the light quark mass, $\delta m_q/m_q = 0.02 \pm
0.04$. Inclusion of the neutron lifetime modification under the assumption of a
variation of the Higgs vacuum expectation value that translates into changing
quark, electron, and weak gauge boson masses, leads to a stronger limit,
$|\delta m_q/m_q| < 0.009$.
