WLS by group size

Hi, Im writing a master thesis where I will examine how the regional economic downturn following the oil price shock in 2014 affected health/mortality in Norway. I will exploit the fact that the economic downturn in Norway following the oil price decline was largely regional, so I will use a differences-in-differences strategy to identify the causal effects.
I was thinking that I should use WLS in my regression, because OLS gives all the observations the same weight, meaning observations from populous counties are given the same weight as observations from less populous counties. But I would like to give more weight to the populous counties.

How do I do this? Do I use aweight or pweight, and how do a generate my new variables? Should I multiply them by the square root of the population size in the county or divide (or something completely different?) And should I weight all the variables in diff-in-diff? (interaction variabel: treat_post in the attachment)

All my data is individual register data aggregated up to county level. I have quarterly data from 2011-2017.
I have uploaded attachments of the varibeles I created to run diff-in-diff (I will be using xtreg/xtdidreg later), and of the regression.