Hum, no, I did see some studies about print fonts, but I don't remember any about screen fonts (the issues being slightly differents).

But at least for me, regularity is important in a font, if we take http://80000hours.org/blog/11-health-vs-education for example (which I found the content to be interesting), and the word 'donations' in the second line, it seems to me that the letters "d", "o" and "s" are bigger than the other letters, which make it feels a bit like DOnatiOnS and is painful/distracting to read.