The gating effect achieved by an ionic liquid and its electric double layer allows for charge transfer which can be an order of magnitude larger than with conventional dielectrics. However, the large charged ions also causes inevitable Coulomb scattering in the conducting channel formed at the interface, which can limit the carrier mobility enhancement. In this work, we study the effect of the LaAlO3 thickness on the transport properties in LaAlO3/SrTiO3 heterostructures by ionic liquid gating. We find that the transport properties of the LaAlO3/SrTiO3 interface are dominated by the intrinsic interactions rather than the LaAlO3 thickness and possible effects from the ions in the liquid. We observe a Kondo effect, which is enhanced while increasing the gate voltage. We also observe a gate-tunable and temperature-dependent anomalous Hall effect, which always emerges near the Kondo temperature. Our experiments pave the way to manipulate the various magnetic interactions in LaAlO3/SrTiO3 heterostructures.