Adapting weights for a glm() binomial regression in R

I've been facing a common problem in R. I can't use my dataset’s weights to estimate a binomial family model. I've been using the glm() function to estimate a probit model, but when my weights variable is added (as an argument in the function "weights = variable.name") the model doesn't converge and my results fall far from what it's expected (). I believe that the problem resides in the form of Weights variable, as the function's document states that binomial family uses the Weigths variable in a different way. When I use Weights for simple OLS with glm() function, it works perfectly.

My dataset explanation for weights: “…this weight was obtained by adjusting an initial weight given by the inverse of the effective sample fraction.” – full text

Glm() doc explanation for Weights: “Non-NULL weights can be used to indicate that different observations have different dispersions (with the values in weights being inversely proportional to the dispersions); or equivalently, when the elements of weights are positive integers w_i, that each response y_i is the mean ofw_i unit-weight observations…”

Glm() (for binomial cases) doc explanation for Weights : “…. For a binomial GLM prior weights are used to give the number of trials when the response is the proportion of successes: they would rarely be used for a Poisson GLM.” – full text

I believe this topic is also discussed here

Is there a way to use these weigths I have in hands to correctly estimate my probit model? Or is there a theoretical obstacle for this? (In this case, how can I weight my regression?)

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