You could argue the QOI is something else (the sum or difference, or even the ratio estimator reported in the title). Margins of error on ratio estimators are quite a bit larger because of numerical properties of ratios.

Since there is interest, I ran a quick simulation[3] to derive the CI of the ratio estimate above ("5x"). By Monte Carlo and using standard assumptions, the confidence interval on the "5X" quantity of interest is 4.51 - 6.82x calculated via the quantile method.[4]

The confidence interval is not appreciably smaller in magnitude if you double the sample size, we're well past the point of diminishing returns.

[1] Weighting would induce a design effect, but here I would suggest that the real problem is a poorly defined population and sample frame, not sample error. This is the real issue here: we have zero reason to believe these 1,000 people are a random sample of any interesting population.

[2] For a parameter \theta = 0.5 -- uncertainly decreases as the statistic becomes further from 0.5. But classical MOEs overreport like this.

[3] R Code on Pastebin: https://pastebin.com/raw/UjHg7qnR

[4] Similar results come from taking the numerical sd of the sampling distribution and calculating a NACI about the mean, I just did the quantile trick because it's less code.