Question: I've often heard that the obesity of women in baroque art signs that such women were the ideal of beauty. How could we know that? And how could we know it wasn't just "cultural rationalization" of a standard physical appearance of higher classes?

Answer: 
A lot of the paintings were commissioned as portraits, why would people pay for themselves to be depicted in an ugly way? 

Wealth nowadays is associated with a slim, tanned, and shaped body because those are traits of people who have enough free time, and money to achieve it. In that period, it would be the reverse, being more on the fat side would require wealth, and more refined foods which were more expensive, while majority of commoners would be slim, tanned (for working in the sun) and toned due to hard work. 

It makes sense based on those, that it must have been acceptable to be fat back then, even desirable.
The idea that, taken across the entire range of media and works, art from any given period represents a society or culture's ideal for how anyone - male or female - should appear has no real basis in fact.

It is vastly more likely - especially in any time frame where we know the names and personalities of the artists being discussed - that any given work represents an example of what *the artist* considered *technically* interesting or challenging, or important in some other way by the standards of his craft or in the judgment of his contemporary artists. This was true even in portraiture.

Three centuries of artistic technical fascination with chiaroscuro *alone* should show us this. Artists chose bodies, poses and themes which allowed them to explore the interaction of light and shadow and the human body; and they did so for technical (and aesthetic) reasons that only rarely had anything to do with depicting ideals of physique.

For most of the history of representational art across all cultures, in fact, there was little attempt to make the figures depicted realistic in any way - "beautiful" or not. Nobody would argue that Greek sculptures from the Geometric or Archaic periods represent the cultural ideal of male and female physical beauty of the time, or that medieval weavers of tapestries or illuminators of manuscripts were attempting to depict the perfect human form.