Let me start by saying I'm not highly skilled in tray design and its something I typically leave to the experts.
In general, increasing the number of flow paths increases the weir length, which has the effect of decreasing the liquid loading per length of weir. It also decreases the liquid flow path length. Multiple pass trays can be used to decrease the tray pressure drop in high liquid rate towers.
Also, as liquid flows across a tray a liquid head develops to overcome the friction between the froth, the tray, and the rising vapor. This can result in a liquid gradient where liquid height is uneven across the tray deck from downcomer outlet across to the downflow weir. Liquid gradient problems become more severe in large diameter towers where flow paths are longer. This is why large diameter trays are usually designed with multiple flow paths to reduce flow path length and the resulting liquid gradient. A high liquid gradient can lower tray efficiency as vapor preferentially flows up through the regions of a tray with a lower liquid/froth height. High liquid gradient can also result in worse weeping at points in the tray where liquid is deeper, closer to the downcomer.
The general rule of thumb type numbers I've heard for this is that flow path lengths over 6 feet can start to create significant gradients, and flow path lengths over 9 feet are to be avoided.