If I am looking to do a factor analysis should I use the weighted data or the unweighted data?

I am looking to do a factor analysis and I have been told that I should use unweighted data. I have also been told to use weighted data. I am looking for some guidance.

As your question indicates, this is a relatively unsettled topic. I’d say the answer depends on the characteristics of the statistic you wish calculate. If you intend the correlations in the factor analysis to reflect population-level frequencies, then you should incorporate the sampling weight. On the other hand, if you intend the correlations to reflect raw frequencies in the sample, then not using sampling weights may be defensible.