> A fat person works harder exercising than a fit person.
Primarily because of improper muscle activation, and from their body weight making the exercise more intense.
Athletes increase their cardiovascular and metabolic throughput (i.e., allowing them to burn even more calories and thus work even harder), and repeating an activity increases muscle control, allowing more coordinated and balanced movements (e.g., keeping themselves and external weights balanced without erratic, wasteful compensatory movements). They might also have a diet that absorbs better, as athletes try to absorb absurd amounts of calories.
A larger person does have a higher base energy consumption, although this is not caused by inflammation - it's just that any tissue need energy. If this was not the case, even just a few kilocalories overeating would cause unbounded growth - instead, energy requirements for a person lie on a curve, and slight overeating for one body weight just means that you reach equilibrium at a slightly higher body weight, with any combination of food intake + activity + body composition having some (although possibly absurd) body mass equilibrium. Of course, being morbidly obese does introduce high risk of certain diseases that have an energy cost and waste (e.g., mismanaged diabetes and sugar in urine), but I consider that somewhat separate.
Caries in = calories out is a thermodynamic problem. Thermodynamics account for inefficient processes. If you take fewer calories in, it always means that your body will be doing less or taking its energy from elsewhere. The body has plenty of ways to do this, including reducing base metabolism at certain costs. The sheer number of backup plans the body has available for any particular function is fascinating, but they are generally all costlier than the primary ones.
However, do not let that deter you from exploring this further. Collecting data on health outcomes of human behaviors is almost impossible without massive datasets - can't exactly cage people up in labs to test them.