The op? Someone actually cares about answering a GQ op? Huh. Wonders never cease!
It is a interesting question to try to answer, and yes the psychological is very real … but not what I think the op was asking about.
FWIW I’ve been mulling it around some more.
In terms of work being done the answer is the physics work and the op is indeed accomplishing the work of carrying 280 pounds up and down those flights, lots more than a 150 pound coworker is carrying. And that is a very valid answer.
And our op produces that work with less perceived effort expended compared to what 150 pound coworker would experience carrying that same total weight, even one who has been climbing stairs for a while (so has muscles well adapted for that activity). Put 130 pounds in a backpack on that coworker (or a 130 pound teenager carried piggyback style) and that coworker would struggle more getting up and down than our op would.
Of course that is both because that a while a significant portion of the op’s weight is fat, there is also a fair amount of the op’s weight that is muscle mass adapted to carrying that mass around, and because the mass in a backpack (or teenager) is not distributed in a way that makes carrying it as efficient.
That perceived effort (sing/talk test as one simple way to keep track) would fairly tightly follow the actual amount of metabolic work being done, which could be measured in a lab condition as the amount of oxygen consumed per minute which in turn correlates with calories expended.
But there is no clear formula to quantify that based on the weight information alone.
As to all the hijacks. Yeah simplistic assumptions lead to simplistic conclusions.
Calculated estimates of BMR and RMR based on body weight alone, even BMI alone, are +/- huge amounts, often reported as 20%, and sometimes much more (in comparison with the gold standard of indirect calorimetry).
RMR varies in response to body weight and composition changes and in response to sorts of exercise done. So even if an accurate RMR was obtained at the start it changes in a nonlinear fashion that is hard to predict, inconvenient to measure, and impossible to calculate.
Calories listed for foods are often very off from their net metabolic impact. A decent discussion of how that happens here but yup, often off by as much as 25%, with the real net to the body calorie impact of higher protein and fiber foods being overestimated.
No question that exercise impacts body composition to great degree (% body fat and how much fat is located in the most health damaging areas), has less impact on total weight loss per se, is of tremendous impact on health regardless of weight loss, and is a key part of maintaining a weight loss achieved.
Not going to go through all those letters but slavish attention to calculations (even if the numbers going in were good, which they are not) misses the key confounder: the role of the brain in all this, and I am not talking about “will power”. Not the psychologic as much as the neurophysiological. The brain is the boss of our metabolism and the brain responds to both the pleasure (“hedonic”) value of food, and its ability to give a sense of having had enough (“satiety”). Any given person will be able to achieve and maintain weight loss better eating a larger proportion of foods of moderate hedonic and high satiety values and relatively little of high hedonic and low satiety level. The former includes higher protein and fiber foods, the latter more highly processed crap. Good review here.