How to determine weights for weighted average? I have some survey results where one of the metrics I am evaluating is being looked at on the state-level (i.e. comparing Delaware's average score of 79% to Virginia's average score of 52%). The sample sizes of these two states are very different (DE has 200 observations, Virginia has 1200) I want to calculate the weighted average score so that I can compare the two states without their scores being swayed by very different sample sizes.
I understand the general concept of how to calculate weighted average, but I am having trouble wrapping my head around how to determine the weights. I have seen some info on using the z-score as the weight, but not sure if this is a statistically sound method nor how it would be helpful as it would be applied to each individual observation rather than a uniform weight for each state (i.e. weight VA by 0.25 vs DE by 0.79). Any advice that can be offered would be greatly appreciated!

Amending original answer. To see how to compute a z-score for comparing two proportions do a search on "compare two proportions statistical test"
===Original Answer===
For a weighted average over the two states you could simply find the average score for the 1400 respondents that reside in Virginia or Delaware.
If you lack the raw data, consider that Virginia contributes 1200 / 1400 = 6/7 of the response between the two states while Delaware contributes 1/7 of that response. So a weighted average would be
52% * (6/7) + 79% * (1/7) = about 56%
