The study focuses on the relationship between species' minimum range size and body size, which has been previously shown in several taxa. The authors test the pattern on freshwater fishes, and attempt to explain such pattern looking at the spatial synchrony in demographic trends. They hypothesize that the increased synchrony with body size explains the increased minimum viable range.
They use many time series and find a similar pattern between body size and spatial synchrony. They conclude that spatial synchrony may underly the body range-size pattern, and propose to use such relationship to support conservation assessments.
Overall, I enjoyed the reading the article, it is well written and presented, and the analyses are robust. The results are novel and make an interesting contribution to ecological theory.
My main concern is the heavily conservation-oriented discussion, which in my opinion is exaggerated and not needed. First, the number of species on which the synchrony could be estimated is very small, which prevents broad generalizations. The test is performed on 21 species, but the authors propose a generalization to about 15K species of freshwater fishes. Second, the predictions are not applicable in a Red List context, if not for simple initial screening (among other existing approaches) for prioritization of new assessments and reassessments. I elaborate this more in my comments below.

A reference missing is Diniz-Filho et al. 2005, which tested the range-size pattern on mammalian carnivorans and highlight the relevance for conservation assessments.
Diniz-Filho, J. A. F., Carvalho, P., Bini, L. M., & Tôrres, N. M. (2005). Macroecology, geographic range size–body size relationship and minimum viable population analysis for new world carnivora. Acta Oecologica, 27(1), 25-30.

L. 68 suggest removing "reliable"

L. 84. the range size is not used directly for criterion B, but can be used to estimate the EOO, which is then used to assess species under B1.

L. 87 This is true if range is used as a coarse proxy of total population size. However, the Red List criterion B on EOO is used as a proxy of risk spread, which is independent on the population density of the species.

L. 192-194: This approach risks to be sensitive to the definition of the bins, why not a simple quantile regression instead?

L. 314: Is this also true in fishes? The citations provided do not refer to fishes. Fishes's dispersal is in most cases passive AFAIK, so this mechanism may not apply to your case study.

L. 314-348: In general, it is unclear if the mechanisms that you describe are supposed to explain your results, or similar patterns found in other studies on different taxa.
In my opinion, one point is not clearly illustrated. Large species live at lower population densities, which implies that range size must be larger at equal minimum population size. I also expect that synchrony scales with population density, with rarer species showing synchrony on wider areas than species living at higher densities.
Similarly, I expect that fast life history lead to a reduced synchrony over wide areas. You hint on these two point in lines 337 but these could be more clearly illustrated.

L. 348-351: Is there any evidence of this pattern in fishes? If so, is the slope similar to other groups?

L. 362: In the discussion there is a strong emphasis on the application of such pattern to extinction risk assessments, specifically the RL. I agree that understanding macroecological patterns can support conservation assessments, but I think the authors should down tone most of this discussion.
First, the sample is definitely insufficient to make generalization. The pattern has been shown on 21 species, and is proposed to be applied to all freshwater fishes (~15K species).
Second, Red List assessors cannot categorize species based on estimates that do not conform with RL criteria. The authors should make clear that this approach can in principle be useful to identify species that should be re-assessed, or prioritized DD species for data collection and first assessments, but that cannot be used for assessments.
This point has been illustrated in Cazalis et al. cited by the authors, that discusses that many academic studies propose approaches to assess species under the RL but these are never uptaken because do not conform to RL criteria.
To support their statement the authors show that most threatened species are close to the estimated range-body size relationship (L. 380). This is because, as the authors correctly explain, the majority of these species were classified under crit. B. However, this stems from a classification bias in the Red List. In principle, there should not be a clear link between IUCN RL categories and the relationship. It is perfectly possible that a species is listed as threatened under e.g. crit. A and is well above the line.

The authors have addressed most of my comments. I'm happy with the revised version and I only have very few points for consideration.

Line 87: Remove B2 which concerns the AOO, not relevant which is a quite different concept from range size (EOO is also not the same, but it shares many similarities, and EOO is typically estimated from the range).

I find Fig. 3 interesting in one respect that is not discussed. While similar, the slopes of the two regressions are different. I think it would be interesting to discuss on the implications of such differences for large species. That said, I appreciate that the confidence intervals do overlap substantially though to make clearcut conclusions.

Fig. 4. How can the range size of an extinct species be > 0km2. I guess this is the last known range size of the species, but is hard to tell what this means, as before going extinct the species has experienced smaller range sizes too. What is that measure meant to represent?