Fury reckons a lot different things depending on the time of day it is. Being fat is never beneficial. And Fury is an exception. Look at the greatest boxers of all time and see how many are fat.
Fedor Emelianenko from MMA, arguably the greatest heavyweight had a similar physique.
Re injuries, it's always hard to get the durability back after a serious injury; you need to go from being cautious and protective at one stage to at some point having the confidence to accept the routine pain and niggles that naturally come from pushing yourself. Difficult to get the balance right.