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1

It is a programming error. The fourth argument of glm is weights, not offset. So either use named arguments or add the offset to the formula like + offset(log(population)).


2

With the offset, you are saying that you look at expected infant deaths per member of the population per year with the theoretical possibility of more than one infant death per year per member of the population. Your model for the mean rate of the Poisson distribution is: $$\log E Y_i = {\bf x_i\beta_i} + \log \text{population},$$ which you can rewrite as $$\...


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