Thin films fabricated from solution-processed graphene nanosheets are of considerable technological interest for a wide variety of applications, such as transparent conductors, supercapacitors, and memristors. However, very thin printed films tend to have low conductivity compared to thicker ones. In this work, we demonstrate a simple layer-by-layer deposition method which yields thin films of highly-aligned, electrochemically-exfoliated graphene which have low roughness and nanometer-scale thickness control. By optimising the deposition parameters, we demonstrate films with high conductivity (1.3 × 10⁵S/m) at very low thickness (11 nm). Finally, we connect our high conductivities to low inter-nanosheet junction resistances (R_J), which we estimate at R_J ~ 1kΩ.