One profitable income-enhancer for sideshow entertainers was to sell small, post-card sized "cabinet cards" with their own images. Visitors could buy these cards as they exited the tents, sometimes signed by the performers. These marketing tools served as souvenirs and free publicity. Many survive today, and these numerous cards open a small window into the ways in which entertainers chose to present themselves.
One thing which appeals to me about late 19th/early 20th century cabinet cards is how dignified the men look.
Circus fat man Egon Cannon and his brother.
New York photographer Charles Eisenmann and his assistant/successor Frank Wendt made many posed studio images of sideshow entertainers, such as George James (below.) A large collection of Eisenmann photos has been amassed by the University of Syracuse in New York.
These Gilded-Age era photographers also produced nude images of their entertainer subjects, such as Chauncy Morlan (whom I wrote about earlier.)
I don't suspect these nudes were for general circulation. But I think there must have been curiosity about fat people, especially as the sideshows often featured "fat families" (not necessarily related in real life) or "marriages" like the Fat Lady and Skeleton man (or a fat couple.) No doubt there was a certain amount of prurience ("How do they ... do it?") Even the attitude of curiosity, however, seems to me better in some ways than over-medicalization.