Such as the body will take the energy to burn fat for recovery, or weight lifting on an empty stomach? Or does it not work like that?
Yes, but not in the way you're thinking.
If you look at something like powerlifting, then carrying additional pounds can be a benefit as they provide either a counterbalance to the weight being lifted (deadlift or squat), or act to shorten the range of motion of the lift (bench press).
There are also strongman events where being on the larger side can be a benefit. Something like the continental press is made easier if you've got a gut to rest the bar on to switch grip. Likewise, atlas stone lifting can benefit from additional bodyweight to act as a counterbalance when lifting the stone from the ground.
Larger people (those with excess body fat) do tend to naturally be stronger than skinnier people, probably due to having to carry additional weight around all day. Obviously there is a limit to this and it does assume you actually move around. If you're 600 lbs and live on your sofa, then you're not going to be getting much benefit from it.