  We follow our previous paper on possible cosmological variation of weak scale
(quark masses) and strong scale, inspired by data on cosmological variation of
the electromagnetic fine structure constant from distant quasar (QSO)
absorption spectra. In this work we identify the {\em strange quark mass} $m_s$
as the most important quantity, and the {\em sigma meson mass} as the
ingredient of the nuclear forces most sensitive to it. As a result, we claim
significantly stronger limits on ratio of weak/strong scale
($W=m_s/\Lambda_{QCD}$) variation following from our previous discussion of
primordial Big-Bang Nucleosynthesis ($|\delta W/W|<0.006$) and
  Oklo natural nuclear reactor ($|\delta W/W|<1.2 \cdot 10^{-10}$; there is
also a non-zero solution
  $\delta W/W=(-0.56 \pm 0.05) \cdot 10^{-9}$) .
