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I have a good working knowledge of how the loess model works but am curious as to how weights work in conjunction with the model. Obviously, this method weights locally, but many statistical packages (I use R) have an optional weights parameter. How exactly do these weights work and what are suggestions for using them?

I am attempting to use sample size as a weight (someone has asked & answered a question on this here if interested: https://stats.stackexchange.com/questions/212518/weight-values-by-sample-size-in-a-loess-regression-in-r). But I would also like to use a categorical variable (3 levels) as a weight as well. Is it possible to do both? How would this effect the model? Any suggestions for the use of this (or particulars to use in R)?

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