You got it. Adjusting for pop density without adjusting for obesity would be a way to favor blue states. Just don’t count me as advocating that position.Again your only looking at one factor, there are economic and education factors. The great irony is you want to adjust for population density because it favors blue states.
My gut is you need to adjust for all four. Or restrict your analysis to more comparable places. The correlation between politics and population density is just too strong. You can do good work, thinking you are looking at one, and it turns out you’re really seeing the other.