I'm working on an ecological study, where I've got 10 years of data for all 3000+ counties in the US. I'm interested in different perspectives on whether in a study like this one should weight the counties based on their population (of interest). More specifically, I'm modeling the relationship between drug prevalence and other characteristics among the general population, so I could weight the counties by their total population. Clearly, weighting will give dominance to urban areas and diminish the influence of rural areas on the estimates.
From my perspective, whether or not to include the weights depends on the research question of interest. If one is trying to get a national estimate, then weighting by population would be appropriate. If one is trying to describe the "average" county, then I'd suggest not using weights, so that each county is treated equally.
I know ecological analysis is done in a variety of fields, and I'm interested both in what people think in general, and then what is common practice in different fields. I'm working with public health experts, who generally have an epidemiological frame, but the work also crosses over into other social science fields.