A warning is triggered when one or more features has more than 1000 neighbors. The default threshold value is 1000, but you can change this by modifying the warnNumberOfNeighbors variable setting in <ArcGIS>/ArcToolbox/Scripts/WeightsUtilities.py.
Performing analyses using a Conceptualization of Spatial Relationships that results in many features having hundreds of neighbors can lead to out-of-memory problems. If a tool is taking too long to run or fails due to an out-of-memory issue, try changing your Conceptualization of Spatial Relationships so that features will have fewer neighbors. The Generate Spatial Weights Matrix tool, for example, offers the K Nearest Neighbor conceptualization which would allow you to specify an exact number of neighbors.