I have a set of cities ranked 1-10 based on several criteria. I also have the percentage of the total population living in these cities. I want the cities with smaller populations to be able to compete with larger cities, so I want to give the population percentages a weight that will compensate for smaller population size. How do I do this?
It's still not perfectly clear exactly what your methods are, but you can normalize on city population. Say B (for big) has 200 stores and 100,000 people while S (for small) has 14 stores and 10,000 people. A simple normalization is to divide store count by population size. focus(B) = 200 / 100,000 and focus(S) = 14 / 10,000. Then you can say the focus score for some city is the number of stores per person. Or you can reverse the fraction to get the number of persons per store. But this effectively reverses your measure. So be careful which you choose.
One would usually weight according to population size to give smaller cities less importance. In your case you don't want to give them less importance.
So don't weight your values.
If you don't put any weights into the aggregates you're computing, that is effectively treating them equally.
Did I understand your question correctly?