  Weakly ionized protoplanetary disks (PPDs) are subject to
non-ideal-magnetohydrodynamic (MHD) effects including Ohmic resistivity, the
Hall effect and ambipolar diffusion (AD), and the resulting magnetic
diffusivities ($\eta_O, \eta_H$ and $\eta_A$) largely control the disk gas
dynamics. The presence of grains not only strongly reduces disk ionization
fraction, but also modify the scalings of $\eta_H$ and $\eta_A$ with magnetic
field strength. We derive analytically asymptotic expressions of $\eta_H$ and
$\eta_A$ in both strong and weak field limits and show that towards strong
field, $\eta_H$ can change sign (at a threshold field strength $B_{\rm th}$),
mimicking a flip of field polarity, and AD is substantially reduced. Applying
to PPDs, we find that when small $\sim0.1$ ($0.01$)$\mu$m grains are
sufficiently abundant [mass ratio $\sim0.01$ ($10^{-4}$)], $\eta_H$ can change
sign up to $\sim2-3$ scale heights above midplane at modest field strength
(plasma $\beta\sim100$) over a wide range of disk radii. Reduction of AD is
also substantial towards the AD dominated outer disk and may activate the
magneto-rotational instability. We further perform local non-ideal MHD
simulations of the inner disk (within 10 AU) and show that with sufficiently
abundant small grains, magnetic field amplification due to the Hall-shear
instability saturates at very low level near the threshold field strength
$B_{\rm th}$. Together with previous studies, we conclude by discussing the
grain-abundance-dependent phenomenology of PPD gas dynamics.
