Why did he look that weird?
This has been a question that has come up more than once in research. Some have pointed to genetic or endocrine disorders such as Frohlich's Syndrome, Prader–Willi syndrome or Klinefelter's syndrome. While these disorders have similar physical characteristics there are many of the secondary issues that do not line up wth Akhenaten's actual life. Both, for example, cause infertility/sterility but Akhenaten had six daughters. Other issues would be characteristics of Frohlich's such as vision problems and increased if not out of control appetite. Prader-Willi, in addition to appetite issues, shows motor problems, scoliosis, speech problems and so on. Klinefelter's is linked to learning disabilities, poor memory, problems with attention and so on. Nothing in the records show these weaknesses. So, either this was very well disguised or the priests of Amun decided not to point fingers at the weaknesses in the person they loathed. This is highly unlikely so we have to look at another explanation.
One explanation put forth by John Wilson is that art was already changing, drifting away from the iconic and structured illustrations and statues to something more relaxed. We can see this increased realism in the following to pieces. One is a horse sculpture from the time period and the other a statue of Haremhab which shows a much "fatter" man than we would expect in a sculpture in the rest of Egypt's history. When Akhenaten's dynasty was deposed (and erased as much as possible) temples and priests vehemently returned to the classic style some of which occurred by the decree of Tutankhamen. One thing that does support the idea that this might be a change in artistic styles is that other tombs of officials and nobles from the time show the same odd head shape and rounder forms.
So if it wasn't a disease and it was artistic why that look? Is there precedence for this kind of look?
There is a precedent that could be applied in the mythology. Hapi, god of the Nile, its bounty and floods (not to be confused with Hapy the son of Horus) shows some of these body features. He has long legs, fatter body, "breasts", rounded buttocks and other features attributed to Akhenaten. This hasn't been definitively proven or dis-proven so I will leave it to your judgement.
|Hapi as portrayed by Amenhotep III, Akhenaten's father, in Luxor|
Two statues of Akhenaten showing the similar body types between Hapi above and the pharaoh.