Ribbons in two-ribbon solar flares can elongate in time, and it is thought that this phenomena is associated with the coronal magnetic reconnection during the flare spreading out spatially in the direction normal to the plane in which reconnection occurs. Most theoretical and numerical modeling work on understanding the mechanisms and speed for the spreading of reconnection have employed current sheets of uniform thickness, but it is unlikely that coronal current sheets undergoing reconnection have this property. We develop a first-principles scaling theory of 3D spreading of collisionless anti-parallel reconnection in current sheets with thicknesses that vary in the out of plane direction. A key result is that the spreading in non-uniform current sheets is slower than the speed of the current carriers in the thicker regions of the current sheet, which is the expected speed from the prevailing theory for current sheets of uniform thickness. We confirm the theory via a parametric study using 3D two-fluid numerical simulations. The results are potentially important for understanding two-ribbon solar flare observations, including why the observed spreading speed is typically sub-Alfvenic.