The proverb is born out of a necessity to highlight and prioritize qualities that can sustain a good life. It uses the imagery of a man with a big belly but who is similar to the small child who has a big belly but does not know where the food comes from. But as a man, one must be able to fend for himself and others and must be accountable for the processes that lead to a good life. Hence, the contrast of growing the heads as opposed to growing the stomach is meant to show the importance of wisdom over appetite. It is not an incrimination of those who posses both or simply have a big belly. It is meant to encourage hard work and clever/strategic thinking over a lavish appetite.
The proverb is applied on people who show an appetite for food or good things/living, to remind them that it better to seek wisdom and intelligence to be able to attain and sustain the good things in life by moral and legal means rather than to merely harness an appetite for those things. It is also used to teach young men to persist in their quest for wisdom. It is not a very diplomatic proverb hence should between those who are in good terms or where there is an advisory role or in a jocular manner lest offense taken may lead to lesson lost.