I am still a bit unsure if I understand, so you are observing some values (weighted, normalized counts data), which is a transformation of some base number (the base number of people sampled). I would say if this transformation is deterministic, then this two values (the observed and the base value) contains the same information, you can just model one of them. If this transformation is stochastic (e.g., k ~ Binomial (n,p)) or with unknown parameters (eg a linear function with unknown coefficients), then you can model the parameters of this transformation in the model.