  The linear growth rate and saturation level of magnetic fields for Weibel
instabilities driven by ion temperature anisotropy, defined as
$\alpha=(T_\perp/T_\parallel)-1$ where $T_\perp$ and $T_\parallel$ are ion
temperatures perpendicular and parallel to the wave vector, are derived in the
small $\alpha$-limit. It is shown that the ratio of the saturated magnetic
energy to the initial ion energy scales as the fourth power of the electron to
ion mass ratio, $m/M$, for an initially unmagnetized plasma with $\alpha\leq
M/m$. Particle-in-cell simulations confirm the mass scaling and also show that
the electron energy gain is of the same order of magnitude as the magnetic
field energy. This implies that the Weibel instabilities cannot provide a
faster-than-Coulomb collisionless mechanism to equilibrate ion-electron plasmas
with ions initially much hotter than electrons, a key component in
low-luminosity astrophysical accretion flows. The results here also show that
the large $\alpha$-limit formulae used in the study of magnetic field
generation in collisionless shocks are only valid if $\alpha\geq M/m$.
