What's more unrealistic, having one size fits all body build or having slightly yet noticably ones? Look at medieval paintings that depict rural scenes. I'd be pleased to hear from you if you have any points you wish to raise.
Paintings are not necessarily an accurate reflection of life at the time. Considering that rich people tending to commission paintings, and rich people would have a higher chance of being fat, it makes sense if they ended up in a painting. Also, a quick google search then wiki walk reveals little in the way of fat people in rural medieval paintings. Perhaps you are thinking more in terms of the
Renaissance which did have some overlap with medieval art beginning in the 1400s. (And if by fat you mean 'not wafer thin' then that could also be include body types that are not necessarily fat in the category of 'fat'.)
The term medieval covers quite a range in history, specifically the 6th to the 15th and perhaps 16th (500s-1400s or 1500s). Paintings differ stylistically by region and time period. One thing I do not see and have not seen are an abundance of fat people in medieval art. Quite the opposite in fact. While they are by no means absent, they were not common.
Medieval diets were also not very calorie-packed. Meat was for the upper classes. And unless you had someone doing everything for you and moved very little, it would be difficult to pack on weight. Doing everything by hand isn't forgiving.