This stuff does get a bit complicated! There are really two questions. First, how much power has to be applied to the cranks to go a particular speed. It depends on the headwind, the slope, the rolling resistance of the tires, the aerodynamic resistance of the person and bike, the weight of the person and bike, the roughness of the road and whatever suspension there might be on the bike or in the way the person rides.

The second question is, given that a particular amount of power is being generated at the cranks, what is the rate that calories of food energy are being burned by the person generating that power? What I hear sreten and chasm54 saying is that the rate of food energy burn is proportional to power generated at the crank. That proportionality doesn't depend on a person's overall fitness nor on their particular fitness for cycling. That surprises me a bit - I have identified several ways that fitness ought to improve efficiency, i.e. change the ratio between food energy burn rate and crank power. But my proposed tweaks to efficiency could well be negligible.

Of course, a fit person will be able to burn calories much faster than an unfit person, because they can generate a lot more power at the cranks. This means they can go faster along whatever route... given that all the other factors like weight, headwind, slope, etc. are constant. If a person loses weight, then the same power will let them climb a hill faster. If they get more fit too, then they'll have more power available and they can climb even faster.

If you lose 40 pounds and see that your time on a hilly route has improved, it doesn't mean you are generating more power at the cranks!

Here is one of my hilly routes. I weigh 180 lb, my bike is 40 lb, and I carry about 20 lb of lock, tools, spares, etc. I only average about 10 mph but I bet my power at the cranks isn't too shabby!