Description
By default, only a warning is triggered when the number of neighbors for one or more features exceeds 1000. This warning is triggered when the maxNumberOfNeighbors variable setting in <ArcGIS>/ArcToolbox/Scripts/WeightsUtilities.py has been changed from None to a specific threshold value, and a feature exceeds that threshold.
Solution
Modify the maxNumberOfNeighbors variable or change your Conceptualization of Spatial Relationships to reduce the number of neighbors for the features in your dataset. If you only want a warning when a specified number of neighbors is exceeded, set the warnNumberOfNeighbors variable in <ArcGIS>/ArcToolbox/Scripts/WeightsUtilities.py to that value and leave the maxNumberOfNeighbors variable as None.