It doesn't change your question at all, but the Cullen-Harrison Act defined it as 3.2% alcohol by weight, not volume
The key part to all of this is what purpose was there in defining a percentage for what counts as an alcoholic beverage? The 18th amendment didn't define what percentage an intoxicating liquor would be, merely that the "manufacture, sale, or transportation of intoxicating liquors" would be prohibited. The 0.5% ABV limit was defined in the Volstead Act ("[intoxicating liquor is] construed to mean any such beverages which contain one-half of 1 per centum or more of alcohol by volume" [1]) to provide clear limits to manufacturers. FDR campaigned on repealing prohibition, and to quickly authorise the sale of alcohol with a higher ABV required defining a percentage that was supposedly still non-intoxicating, with FDR justifying the redefinition as providing needed tax revenue, while being permissible under the constitution as non-intoxicating [3].
The Cullen-Harrison act definition of the limit of non-intoxicating was originally expected to be 2.75%, due to a "general consensus" that it was not intoxicating, however this was increased to 3.2 because "the beer provided for in the bill is of a slightly higher alcoholic content, and being more palatable, would be consumed more generally than 2.75 beer" [7]. Brewers insisted that 3.2% ABW was non-intoxicating during hearings for the Cullen-Harrison act [4], and to be on the safe side, brewed beer at closer to 3%.
As a footnote, and potentially what framed the limit, the range of ABV percentages for small beer is 0.5%-4.2% [5]. Small, or table, beer lacked the stigma of stronger liquors [4], and in fact, using George Washington's recipe for small beer resulted in an ABW of 3.2% [6].
Edit: added a source why 3.2%.
1 - https://www.historycentral.com/documents/Volstead.html
2 - https://www.law.cornell.edu/constitution/amendmentxviii
3 - http://www.fdrlibrary.marist.edu/daybyday/resource/march-1933-6/
4 - https://books.google.com/books?id=KUxWDwAAQBAJ&pg=PT53&lpg=PT53
6 - https://www.homebrewtalk.com/forum/threads/george-washingtons-small-beer.429161/
You sent me down the rabbit hole tonight, but I think I've got your answers! First time posting in this sub so I hope I did the citations, etc. correctly.
My first find was that the National Institutes of Health (NIH) said it was based on scientific studies at the time that found that initially 2.75% and then later as high as a 3.2% alcohol level was low enough to prevent someone from readily getting intoxicated while drinking these beverages. Mentioned through the NIH's site HERE But naturally I wanted those studies!
To find detail, I looked around and found plenty of medical testimony that makes it clear that there was consideration and research into "Exactly how much alcohol by volume can make someone drunk?" in the decades before the 3.2% number ended up in law. For example, on page 175 of this report as far back as 1919 you have doctors talking about studies showing that 2.75% beer was too low to be intoxicating and so shouldn't really be treated as intoxicating liquors.
But, clearly the number inflated over the years to the 3% plus, and the cause of that seems to have been experts like Professor Yandell Henderson. As the Senate was grappling with a desire for beer across the country in the 1930s, Henderson testified to Congress about experiments and studies performed to find what level of alcohol could cause intoxication. This journal piece describes the evolution of those studies HERE. In short, he found that levels in the 3.2% range were perfectly acceptable. I even found pictures of Professor Henderson testifying and seemingly showing the Senators alcohol. HERE
EDIT: Also worth noting that by this time, President Roosevelt himself was demanding that Congress legalize this low-alcohol beer. I found a UPI clipping from the time. See it HERE.
This article also points out that this being the government and all there was a financial aspect at play that I couldn't quite flesh out but seems relevant- they wanted to legalize alcohol to tax it and fund government programs. I started digging through the Senate Finance Committee's historical record to find the actual debates around the beginning of re-legalization of higher alcohol beer and what you will find are Senators eventually debating the issue not from an intoxications standpoint but from a revenue standpoint. In essence, they were asking: how much alcohol do we have to allow into these drinks to make them marketable, and therefore taxable, and therefore a source of revenue for the government? For example, you see them HERE doing just that, though seemingly more on the wine front.
Hope this helps!