Sorry, by normalized I mean taking the observed weighted data and dividing by the size of the population. The contribution of each member of a sample towards the observed data is unknown and different for each member.
As an example, for an event I am told that of a population of 1 million people, a sample of 34 people attending the event was taken and that after weighting there were an average of 40,500 people of that population in attendance per minute of the event. The value I am told was observed for the event is then 40,500 / 1,000,000 = 0.0405. Thus, without knowing the weight each person in the sample contributed to the value, I want to place uncertainty around the value of 0.0405 proportional to the amount of people that were used to form the sample.
Hopefully that’s clearer.