We induce surface carrier densities up to $\sim 7\cdot 1014$cm$\mathrm{<mrow\; data-mjx-texclass="ORD">-2</mrow>}$ 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 $\sim 1013$cm$\mathrm{<mrow\; data-mjx-texclass="ORD">-2</mrow>}$ to $\sim 7\cdot 1014$cm$\mathrm{<mrow\; data-mjx-texclass="ORD">-2</mrow>}$ 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.