You are working with different populations, I don't see any other way to compare your results. All the populations (5 - 6000) are coming from a population, you will have to trust your instincts to test if they are dependent or independent. But I would suggest that you treat these as separate samples.

You can try conducting a two sample t-test between varying percentages i.e. number of women expressed as a percent of total population.

Intuitively, what you are trying to accomplish does not make sense. In the example that you have given, you don't really know the relation between populations of Northern US and Southern US. You can't say with absolute certainty that they are independent or dependent (and how much dependent).