Does one "burn calories" by unloading a truck? If I exercise by weightlifting, I can "burn calories". The way I understand the process is as follows: when I'm moving the weight up, the energy from chemical bonds turns into potential energy of the weight. When I'm moving it down, though, the same potential energy turns into heat inside my muscles and ligaments. The heat is then dissipated around - that's why I'm sweating. The same happens e.g. when running, only now the weight is my body.
Now assume that I'm unloading a truck, i.e., only moving weights down. I'm now just using the potential energy to heat my body. In fact, because of this additional heat, I may burn less fat than I would burn at rest to maintain my body temperature. Therefore, if I wand to lose some pounds, it seems I should prefer watching TV on my sofa to unloading a truck. This conclusion is counter-intuitive - unloading a truck seems feels like any other physical activity. So, what's going on here?
 A: To get material off of a truck, you generally must either (a) lift the material off the floor of the truck, or (b) slide the material against the floor of the truck, overcoming friction. Both require work.
If you had a truck where all of the heavy objects were loaded onto pallets, which you could move by lifting a centimeter or less using a pallet jack, and you were unloading to a dock level with the truck bed, you would reduce the work to the tiny lift with the pallet jack and the small rolling friction of its wheels. Much less work than lifting material into the truck from the ground, but probably more than watching television.
Some freight companies use containers which fit neatly into their tractor-trailers, and build trailers whose floors are covered in casters or conveyor rollers, so that a container can be moved to and from a similarly-rollered loading dock using only low-friction horizontal motion. With this kind of setup, a single worker can manipulate a ton-scale freight container — though there are crush hazards if the container gets any significant momentum.
If you must lower heavy objects from a raised truck bed to the ground, your apparatus for maintaining your balance uses many of the same muscles as your apparatus for lifting.
Plus, you have to get your self back up onto the truck after each package you gently unload. A typical box on a moving van is less massive than a person, so most of the work is done getting the mover’s body in and out of the van.
Unloading to the ground gently is much more work (for a person) than, say, pushing the load to a ledge and letting it fall off.
A: To unload a truck you have to move. Ignore the freight being lifted and lowered. Moving your body requires energy. Lifting or lowering weights can't decrease the energy required.

I'm now just using the potential energy to heat my body.

No. You're not extracting energy. Unless you drop the weight onto a lever or something. It takes the same amount of energy to lower a thing as to raise it. That's why unloaders in real life drop anything that isn't labelled "fragile."  If you drop something on the floor then the potential energy is perhaps mostly converted into heat (and/or the sound wave). But that isn't the case with the unloader.  This heat is created because there is fuel being burned to generate that heat and useful work. The potential energy of the weight doesn't transform directly into heat.
It takes energy to merely hold an object:

If I put the mass on a table, the table requires no input energy to maintain the normal force that holds up the mass. The table is doing zero work, requires zero energy input and doesn't seem to get tired. Why the difference? The difference is related to the different kind of molecular bonds involved, and how they vary with displacement. The molecules in a muscle fibre exerting or resisting a force are in an active state, and to stay in this state requires input of the biochemical ATP (adenosinetriphosphate , described often as a cell's energy 'currency'). ATP molecules must be supplied continuously to the myosin head of each muscle filament to maintain a molecular cross-bridge that maintains tension in the filament. To supply the ATP, you must 'burn**' fuel. Not only that, but you also get tired from lowering the brick, because the muscle is still under tension during (controlled) lowering.The bonds in the wood of the table are also biochemical, but they are in a stable state and are only stretched or compressed under load, a bit like a spring. This tiny stretching or compression requires no new chemical reaction and is usually close to reversible. https://www.animations.physics.unsw.edu.au/jw/biological-work.htm

A: If you load your truck by placing each item precariously onto the edge of the lowered tailgate of your truck so that everything is just about ready to fall off, you'll still break a sweat because you've had to lift all those heavy boxes.  The inefficiency of your body in doing that work generates lots of excess heat and your body will react by engaging its cooling system.  You've burned more calories than you've imparted as potential energy because of inefficiency.  As my grandfather says, "it's tough work being a meat bag."
If you then then unload the truck the way a cat would, giving things an infinitesimal tap with your paw, pushing them off the truck and letting gravity do the rest of the work of "unloading", then you are barely putting any energy at all into unloading, and you're not going to break a sweat.  As my grandfather says, "a butterfly fart" would be enough to knock the boxes off.
The potential energy of the box is transformed into kinetic energy as it falls, and then ultimately that kinetic energy is dissipated when the box hits the ground, probably with sound, other disturbance of the air, inelastic deformation of the box, maybe breaking its contents, and maybe even slight deformation of the ground itself.
The box may very well end up right where it started in this story, albeit a little beat up having fallen off the truck.  All the energy of the collision of the box with the ground originally came from you when you imparted energy to the box by lifting it from where it started onto the truck.
Everything else (in terms of you burning calories and sweating) can be attributed to inefficiency.
A: 
If I exercise by weightlifting, I can "burn calories". The way I
understand the process is as follows: when I'm moving the weight up,
the energy from chemical bonds turns into potential energy of the
weight. When I'm moving it down, though, the same potential energy
turns into heat inside my muscles and ligaments. The heat is then
dissipated around - that's why I'm sweating.

I think a biological perspective might help here. When you activate your muscles, they use a molecule called ATP as "fuel". When the ATP is used, it releases chemical energy. Some of that energy is used in the actual muscle contraction, but the process isn't 100% efficient, so a lot of that energy is wasted as heat.
It's like burning gasoline in a car. Some of it is used in the actual function of the car, but if I recall correctly, gasoline engines are only something like 20-30% efficient; the rest is wasted as heat.
On top of that, there is only a very small amount ATP stored in our cells, so our bodies have several mechanisms for producing it as needed (e.g., converting glucose to ATP). These processes are also not 100% efficient and will produce heat as a by-product (along with other things like the lactic acid that makes our muscles sore).
That's where the heat in your muscles is coming from. There technically is also friction as your muscle fibers contract and your body moves, but I'm not sure it generates a significant amount of heat relative to the chemical reactions.

Now assume that I'm unloading a truck, i.e., only moving weights down.
I'm now just using the potential energy to heat my body.

A physicist might have to correct my physics interpretation here: I think it's correct to say that when we lift an object, we are converting the chemical energy in our bodies to gravitational potential energy in the object.
When we lift an object, we use chemical energy to activate our muscles. When we lower an object, we are still using chemical energy to activate our muscles, but instead of doing it to lift, we are doing it to slow the rate of descent of the object. The heat our body generates comes from the inefficiencies of that process.
If my interpretation of this answer is correct, then it's correct to say that the loss of gravitational potential energy is being converted to chemical energy (Again, I'll let a physicist correct anything here). This is a little unintuitive to me as non-physicist because I think the statement is describing what is happening from a physics/mathematical perspective rather than what is happening from a biology and chemistry perspective.
