Let's say I have a regression of the form:
where $j$ stands for county, and $y$ and $X$ are averages over worker outcomes/characteristics for each county, and $T$ is a continuous treatment variable that varies at county level.
When estimating in Stata I was suggested to use "aweight" option, where analytical weights are derived from county population.
Now I want to include county population as a control variable. Wouldn't this cause a problem as I am already using county population for weights?