Indeed, but in ways much different from what is usually discussed, and from what you (I believe) implicitly imply.

e.g., I've recently discovered that my unexplained weight gain (which over the last year looked like 4-5 step functions, rather than anything continuous) is a result of Niacin (Vitamin B3) deficiency.

That's something I discovered (accidentally) by observing inputs and outputs, the input being B3 supplementation (taken for a completely different matter), which quickly undid all the weight gain (and a lot of other symptoms).

10 or so Doctors (specialists and generalists) and nutritionists have seen me over the last 15 years for my weird weight. Not one ever suggested B3 might be the problem, or ever had a test that would indicate I'm B3 deficient -- although, I have reason to believe I've been deficient for at least 20, and possibly 30 years.

So, yes - observing input and output is definitely enough to control weight. But as this anecdote shows, it's not necessarily the caloric balance, which is what you stated in the first place.

Well it's still caloric balance; just that the mechanism of how that balance occurred changed.

What we're arguing about is the boundaries of causality. Take mental illness. Some people get fat because they have a mental illness. What's the cause of their obesity? Caloric balance or the mental illness?

Depending on the boundaries you draw, one or the other, or both.

I'm not sure I understand your definitions.

Same caloric input, same exercise (that is, main control signal for caloric output the same). Difference in input is a substance without caloric value. Huge difference in weight.

The only caloric balance here at play is the tautological one ("caloric balance was positive as evidenced by gaining weight. later, caloric balance was negative as evidenced by losing weight"). Other than that, assuming you believe this anecdata (which you may not), the notion of caloric balance is useless.

(And, feel free to disbelieve anything I say, but read on B3 and you'll realize there are numerous reports of reduced weight that starts with B3 supplementation, despite no other change in intake or exercise)