Recall that for GLMs, information matrix \(J=X'WX\),
where \(W\) is a diagonal matrix with elements \(w_i=\left( \frac{d\mu_i}{d\eta_i}\right)^2/\text{Var}(Y_i)\) on main diagonal.
For logit link with binary GLM, \[\begin{eqnarray*} &&\eta_i= \log\left(\frac{\pi_i}{1-\pi_i}\right),\mbox{ (canonical)}\\ &&\frac{d\eta_i}{d\mu_i}=\frac{d\eta_i}{d\pi_i}=\frac{1}{\pi_i(1-\pi_i)}\implies \frac{d\mu_i}{d\eta_i}=\pi_i(1-\pi_i),\\ &&\text{Var}(Y_i)= \frac{\pi_i(1-\pi_i)}{n_i}. \end{eqnarray*}\] Thus, \[ w_i=n_i\pi_i(1-\pi_i),\\ W=\text{diag}\{n_i\pi_i(1-\pi_i)\}\\ \implies Var(\hat\beta)\stackrel{\text{asymp}}{=}(X'WX)^{-1}. \]
For Fisher scoring (=Newton-Raphson for logit link), iterative method of obtaining ML estimate solves \[ (X'W^{(t)}X)\beta^{(t+1)}=X'W^{(t)}z^{(t)}, \] where \[\begin{eqnarray*} W^{(t)}&=&\text{diag}\{n_i\pi_i^{(t)}(1-\pi_i^{(t)}) \},\\ z_i^{(t)}&=&\eta_i^{(t)}+\frac{y_i-\pi_i^{(t)}}{\pi_i^{(t)}\left(1-\pi_i^{(t)}\right)} \mbox{ for logit link.} \end{eqnarray*}\]