My guess is it is childhood. I see poor people eating junk food all the time and feed that to their kids - the kids are fat on empty calories and so the brain doesn't get what it needs to grow smart.
That is just a guess though. I don't have the ability to verify it.
There are plenty of fat smart people. The brain does not develop, and especially does not develop knowledge, as a result of the passage of time and metabolic processes. It develops, both structurally and in terms of 'contents', solely as a response to repeated stimulus. We don't really have a word for a situation where a persons life is impoverished due to lack of intellectual stimulus, but we certainly have the condition. Some kids grow up in homes where if they ask a question, they'll get an answer. Others grow up in homes where an asked question is replied to by the parent dismissively saying 'I don't know' (sending a clear message that the child shouldn't want to know) as they turn back to reading about celebrity gossip. No amount of clean eating can overcome that sort of poverty. Internet access can, though.
That being said, insulin resistance / T2DM is associated with the thinning of cortical tissue [0] - insulin resistance being the typical cause of burgeoning fat storage. Additionally, the brain runs well on ketones [1], which are an abundant supply of fuel on the insulin-resistance-reversing ketogenic diet.
All I'm saying is there may be some benefit for the many fat smart people in taking up some kind of insulin-resistance-reversing diet; lo, for all the fat people (, as well as the thin-yet-still-insulin resistant people, too). But ketosis is not exactly the default path-of-least-resistance for most people, given the standard american diet, conventional nutritional 'wisdom', etc.
That is just a guess though. I don't have the ability to verify it.