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Weak lensing data follow a naturally skewed distribution, implying the datavector most likely yielded from a survey will systematically fall below itsmean. Although this effect is qualitatively known from CMB-analyses, correctlyaccounting for it in weak lensing is challenging, as a direct transfer of theCMB results is quantitatively incorrect. While a previous study (Sellentin etal. 2018) focused on the magnitude of this bias, we here focus on the frequencyof this bias, its scaling with redshift, and its impact on the signal-to-noiseof a survey. Filtering weak lensing data with COSEBIs, we show that weaklensing likelihoods are skewed up until $\ell \approx 100$, whereasCMB-likelihoods Gaussianize already at $\ell \approx 20$. WhileCOSEBI-compressed data on KiDS- and DES-like redshift- and angular rangesfollow Gaussian distributions, we detect skewness at 6$\sigma$ significance forhalf of a Euclid- or LSST-like data set, caused by the wider coverage anddeeper reach of these surveys. Computing the signal-to-noise ratio per datapoint, we show that precisely the data points of highest signal-to-noise arethe most biased. Over all redshifts, this bias affects at least 10% of asurvey's total signal-to-noise, at high redshifts up to 25%. The bias isaccordingly expected to impact parameter inference. The bias can be handled bydeveloping non-Gaussian likelihoods. Otherwise, it could be reduced by removingthe data points of highest signal-to-noise.

The impact of signal-to-noise, redshift, and angular range on the bias of weak lensing 2-point functions