How do you maintain all input raster values in a weighted sum calculation so that the output raster contains ALL of the contributing raster values? It seems like the output only includes a calculation and extent only where ALL of the rasters overlap, and doesn't include the values where there is not a total overlap.
I assume you have already tried to set the extent to the combined extent of the rasters, even if this entails specifying this in the Environments tab from a manual determination.
If you have already tried that, then you may have some work to do.
There is no information in the help regarding nodata values. or differing extents.
I suspect you may have to make copies of the inputs that you want to use, specifying a combined extent. Use a common cell size and snap raster. The no data values could be reclassed to 0, *if appropriate* to enable summation on a cell by cell basis.