It sounds like your polygons have the same outer bound, but are the inner boundaries identical? (For example, counties) Or are they varied by data type? If they are all identical, use a spatial join and combine attributes. If not, you would need to union the lot and then use spatial join.
All that bother can be avoided by converting to raster... Instead of using the weighted overlay tool, use a numeric field to hold your weights; then use the raster calculator to get the weighted output.