I use functions in R as context for the question, but it is more generally about the meaning of two terms used to describe weights applied to cases in regression models.
In lm, the "weights" argument triggers WLS fitting to minimize the sum of the weighted squared residuals. These are called typically called "sampling weights", "probability weights", or "inverse probability weights", as in Horvitz-Thompson estimation.
In nnet, the documentation for the "weights" argument notes that it expects a (case) weight for each example. I'm wondering what this means, precisely, and how case weights differ from the usual probability weights, if at all.
It may be that the emphasis on the word case here is simply used to distinguish the "weights" argument in nnet from the "Wts" argument, which is used to specify starting values for the regression coefficients between hidden and observed nodes.
Any insight about "(case) weights" would be very helpful.