In reply to Kevin.

No, it's not that simple for logistic regression. My previous response was for least squares regression, and I suggest that you understand the simpler linear problem first. For OLS, you will get the same answer for the regression parameter estimates if you multiple each response value by the sqrt(weight) and also each row of the design matrix by sqrt(weight), as I have indicated.

However, for logistic regression the response is binary and the estimation procedure requires solving a nonlinear optimization problem.
You can't multiply a binary response (0/1) by the sqrt(weight) because that will give you more than two response values. Instead, form linear combinations of the (weighted) design columns and maximize the log-likelihood to obtain the parameter estimates.