There is little evidence that BMI affects the effectiveness of birth control pills, the variety of pill and dosage and including ingredients is to address the effectiveness of the prescribee to use the medicine properly and genetics (some people have clotting disorders, some people do poorly on dual hormone medicines, just depends). For example, if you are careful with taking your bcp the same time every day you will do fine on a low dose birth control pill no matter what your BMI is. This is not so true for new mothers or some college women because of their life demands can not ensure they are consistently taking the medicine on time, although it is great in terms of breastfeeding and desiring more children in the future for new moms as it does not interfere with lactation as much as higher dose ones do.
While it is anecdotal as I am one person, low dose birth control pills were completely effective for me for a decade despite always being a large human being and having high fertility when I wanted it (and when I didn't otherwise). So this is a surprise. I doubt it is because fat creates estrogen, the estrogen from fat tends to interfere with ovulation and estrogen peaks with ovulation (the follicle baths the maturing ovum with it) - plan B seems to interfere with both ovulation and sperm effectiveness by creating a more hostile reproductive tract (meaning they don't know for sure how it works). My guess is that plan B is diluted by the body and would be better to place plan B internally in some manner, with a plan B ring for example (placed around the cervix). Remember, BMI describes total weight in relation to height, not necessarily adipose tissue.