Description
TheNeighborhood Type parameter's Contiguity edges and corners option allows neighbors that are connected only at a corner. When weighting by length of a shared border, this distance is zero, and the features will receive a weight value equal to zero and will not be considered neighbors by subsequent analysis methods.
Solution
Use the Pairwise Polygon Neighbors tool to identify any polygons that are connected only at a corner, and determine whether losing these neighbor relationships significantly changes the neighborhoods. If these relationships must be preserved, use a different neighborhood type or weighting method.