Questions on Weighted Least Square Estimation
The linear model is $b=Ax+r$, so you can see the errors $r$ as the noise added to the measurements $b$.
The covariance $\Sigma_b=E\{(b-\bar{b})(b-\bar{b})^T\}=E\{(b-Ax)(b-Ax)^T\}=E\{rr^T\}$
$E\{rr^T\} \neq E\{bb^T\}$ unless $Ax=0$