Given the semantics that make the most sense to me - no one is weak.

No one is "weak" unless they can’t feed themselves or can’t raise up out of a chair even with leaning forward.

But what irritates me is that most of the time when someone is characterized as "weak", they are someone that is in pain or jacked up in some way. The field of medicine will characterize someone as weak if they do not perform a certain way that is predetermined in our training. If a certain muscle is considered weak then most of the time, not always, it is responded to with a plan of strengthening.

If we are actually strengthening, it obviously has to be a certain level of heavy after the movement as been learned sufficiently. However, i'm not sure that we are "strengthening" when the typical loads used in a PT clinic are so low that the heaviest weight is a blue stretchy band. Or when a high school volunteer or tech supervises clients after a 5-minute warm-up on an arm or recumbent bike, staring at a list of exercises on a sheet of paper made by a PT that is typing away on their computer.

But is the muscle actually weak if there is pain? Or, is the muscle weak because there is some form of threat leading to inhibition? Is the muscle weak when the joint is stiff and doesn't allow proper position for force production? How does strengthening fit into any of these situations?

Muscles aren't weak! There are just varying levels of strong.

Systems can be inefficient which can limit force production. Fix the System and then retest your performance - you may be surprised!