  We induce surface carrier densities up to $\sim7\cdot 10^{14}$cm$^{-2}$ in
few-layer graphene devices by electric double layer gating with a polymeric
electrolyte. In 3-, 4- and 5-layer graphene below 20-30K we observe a
logarithmic upturn of resistance that we attribute to weak localization in the
diffusive regime. By studying this effect as a function of carrier density and
with ab-initio calculations we derive the dependence of transport, intervalley
and phase coherence scattering lifetimes on total carrier density. We find that
electron-electron scattering in the Nyquist regime is the main source of
dephasing at temperatures lower than 30K in the $\sim10^{13}$cm$^{-2}$ to
$\sim7 \cdot 10^{14}$cm$^{-2}$ range of carrier densities. With the increase of
gate voltage, transport elastic scattering is dominated by the competing
effects due to the increase in both carrier density and charged scattering
centers at the surface. We also tune our devices into a crossover regime
between weak and strong localization, indicating that simultaneous tunability
of both carrier and defect density at the surface of electric double layer
gated materials is possible.
