We report on resistivity and Hall measurements performed on a series of narrow mesa devices fabricated from LaAlO_3/SrTiO_3 single interface heterostructure with a bridge width range of 1.5-10 microns. Upon applying back-gate voltage of the order of a few Volts, a strong increase in the sample resistance (up to factor of 35) is observed, suggesting a relatively large capacitance between the Hall-bar and the gate. The high value of this capacitance is due to the device geometry, and can be explained within an electrostatic model using the Thomas Fermi approximation. The Hall coefficient is sometimes a non-monotonic function of the gate voltage. This behavior is inconsistent with a single conduction band model. We show that a theoretical two-band model is consistent with this transport behavior, and indicates a metal to insulator transition in at least one of these bands.