"Weight" is a poor control. BMI is a better one. Going back over the study, it looks like the controls are listed in table 2. 12/17 appear to adjust for BMI, with the following note from the authors regarding the resolution: "We were unable to perform a subgroup analysis according to the body-mass index because the mean values were not stated or estimable in the majority of the reports." (emphasis mine) This certainly doesn't throw out the results for me, but I still find myself asking the same question. But moreso the protein vs fat ratio question, as in my reply to the subthread above. With only three macronutrients in play, I can't fathom throwing two of them together.
You are reading way too far into my words when I'm speaking causally, I do not write my comments in the dense and precise language in which studies are written as it's a bit overwrought for casual discourse. I had hoped you would give me the benefit of the doubt that when I said weight you would take that to mean some sort of levelized metric.
The people that do these studies aren't as dumb as you seem to think they are nor are the type of confounding variables you are expressing foreign to them. Not even study can get exactly the quality or quantity of date it wants, that's why its a good idea to look at multiple studies and examine large-scale trends and repeatably, which is the type of studies I linked.
Some of them did only consider weight. It is the conclusion of the meta itself a mean BMI couldn't be determined from the 12/17 that had it. I don't think those running the studies are at all dumb. They are often focused on specific things, and to the exclusion of generalizable conclusions. I do find it odd that even mean BMI wasn't of apparent interest in diet studies, but I haven't gone thru each sub-study to see why or why not.
I wouldn't feel comfortable reading too much into this one's conclusion. "Low-carb w/o any additional specificity looks like bad news" seems technically fair to me, but actual diets are going to tend to distinguish fat and protein as well as their sources so that isn't a a very logical stopping point for an actual decision. Including core concerns like fat vs protein and plant vs animal sources can yield different conclusions, as the meta linked in the sub-thread above did.