This paper scrutinizes the possible violation of some WLS presumptions in empirical projects. In general, for the WLS estimator to be consistent, asymptotically normal and Eicker-Huber-White’s heteroskedastic standard error to converge to a non-random limit, one needs to make sure that the first and second moment of the interaction of weights, regressors, and noise are finite. This paper aims to raise the concern of the contamination of fat-tailed weights in a series of papers that adopts American county or American CZ as its observations and weights the observation by its population. This would compromise the consistency and asymptotic property of the estimator. I used a Monte Carlo experiment to see the potential effects of fat-tailed weights on regressions and proved that under fat-tailed weights, the Eicker-Huber-White’s variance- covariance matrix estimator generally understates the real variance-covariance matrix, and is inefficient. I then take Blanchard et al. (2019) as an example and replicated their work but rezoned their regression observations. In my replication, I found no evidence for the claim that the retaliatory trade shock from China shifts American voters to the Republican Party and this could very likely be a consequence of the fat-tailed weights.