High school physics teacher holding a weight on his outstretched hand said he's doing no "work".
He was expending energy against gravity though.
Physics is often very theoretical (its a good thing, we must understand fundamentals first!).
Human body is a poor study for this. Another poor study example is a helicopter. It just sits hovering, not changing altitude, naive physics would tell you that it uses no energy hovering there. Please tell the helicopter pilot that he doesn't need any fuel to hover.
There are lots of examples of mechanisms that require energy just to be in a static position, but if if you don't factor these complex mechanisms into the equations, the equations will just give you a lower bound of how much energy is needed to do something. Helicopter blades that need to actively be driven to provide a constant supply of air mass to counteract gravity, or human muscles that require a supply of energy to stay flexed, all add components to the equations that make the equations more complex. If you don't include these extra complex components, you will just get lower bounds.
Sometimes lower bounds is enough for engineer to ballpark something. Sometimes its not.
It doesn't require any energy to hold up a weight. Just put it on a pedestal and marvel at how inefficient your muscles are for holding things in static positions. But it DOES require energy to lift a weight against gravity. There is no classical newtonian machine that you could EVER build that will be able to lift an object without requiring some sort of energy input.
But then you might ask for the static case: "Where is all of that energy that i'm putting in going, if not holding up the object". Usually this answer is heat. Flexing a muscle without moving anything ultimately just produces heat. Helicopter hovering produces some kinetic energy in the flow of air moving down, and a lot of heat. Also, a lot of that kinetic energy ultimately transforms to heat later anyways.