Ancient 'female-centered' society thrived 9,000 years ago in proto-city in Turkey
(www.livescience.com)
Not all obesity is solely due to what you eat. Hypothyroidism can cause obesity even if you eat healthy.
Also, most of these fat looking statues are of women. It's important to keep in mind that, back then, they were likely to give birth to 4+ kids (child mortality was high) and pregnancy can cause all sorts of changes in their bodies.
A woman looking like that statuette would certainly be rare, but you could expect to find something "close enough" from a number of women aged over 50 that had many children before menopause.