Should I take logarithm of weights in WLS regressions I am new here.
I have a question regarding the anlaytical weights used in ivreghdfe or reghdfe regressions. People usually take aweights in STATA, my question is how we deal with the weight if the weight itself is highly skewed?
Should we take the logarithm over that or should we drop those outlier observations simply?

No, you should not take the logarithm of analytical weights or drop observations with high weights.
When you use weights in a model, you are telling stata how many people in your population had certain characteristics. If you are using frequency weights, for example, you might have counted 10 people who exercised 1 hour a week, smoked, and had heart disease, and then 40 people who exercised 3 hours a week, smoked, and had heart disease.
When a weight is high, that just means that lots of people in your population had a given pattern of data. If you were to drop "outlier" weights because they were too large, you would be discarding a lot of people from your dataset just because their experience was really common. This forces your model to make inferences on uncommon people, and it tells people that the most common covariate patterns never happened.
If you were to take the logarithm of weights, you would misrepresent how common a given pattern of characteristics was in your population. The model would weight patterns of observations from a group of 200 only a little bit higher than patterns of observations from a group of 100 (because log(200) / log(100) = 1.15) while for correct inference, it needs to weight the pattern of observations from the group of 200 twice as heavy as the group of 100.
Analytic weights as you reference don't work exactly as described above, but the same principle applies. You should not take the log of weights or drop "outlier" weights.
For a summary of weighting methods in stata, see this page
