Some factors that lead to weight gain can include:

Diabetes

Low thyroid

Liver disorders

Many medications

Prader-Willi syndrome and other hypothalamic defects

Some tumors

Let's take for example a women going through menopause. Their diet and activity remain the same yet many women will put on massive weight in a short period of time. Why? Well there is the fact that their estrogen and progesterone ratios shift leading to excessive estrogen to progesterone. And in many cases they also take a powerful estrogen like Premarin. In both cases the estrogen causes the weight gain due to water retention and the suppressive effects of the estrogen on the thyroid. So no input vs output involved.

Then there are drugs such as Prednisone, which is way over prescribed. It also leads to weight gain, primarily through water retention. Again no input vs. output involved.

And what about people with congestive heart failure? Again water retention from inability of the heart to push the blood through the kidneys properly leads to water retention and weight gain. Again no input vs. output.

It would be great if weight gain and weight loss was as easy as you want to propose but reality does not make it that easy for us.