This could be due to a number of factors but probably the main cause here is the high quantity of cells with a zero value (315) in comparison to the other ones. With both methods all values of interest come out as having high residuals. This tends to explain even more why both models have issues with the fitting.
The residuals for the non-spatially weighted regression are presented in figures \ref{483824} and \ref{373705}.  These are almost similar to the ones obtained with the spatially weighted method,  which does not represent an improvement over the OLR here. This is why only one map of residuals is presented. Figure \ref{373705} clearly shows all non-zero values for housing assistance present high residuals.