There was some fat, however much a fraction of body ratio it had become. But there were so many being killed and so rapidly that... well, a little adds up to a lot over time :-/
When the Nazis were burning mass bodies in pits they
found that a ratio of one fat person to two skinny ones
worked well.
At first they just buried them in mass pits but that
didn’t work very well as they swelled up and broke the
surface so later in the war they had to dig them up
and burn the remains on “roasts” or iron racks, trying
to cover up the evidence of their crime.