For instance, I just tried http://caloriecount.about.com/cc/calories-goal.php (after googling it out of the blue) with starting weights of 300 and 200, ten pounds to lose both ways, everything else the same. The calculator suggested the 200 pound guy needed to eat 500 calories a day fewer than the 300 pound guy did.
In other words, suppose the obese guy needs 3500 calories a day to maintain his weight, and the skinny guy needs 2000. Then I guess it might be true that if the obese guy eats 3510 calories a day, he will gain weight faster than the skinny guy eating 2010. That seems counter-intuitive but at least plausible.
In other words, it's not a linear relationship.
That seems to make a lot of sense, actually.
If experimental data says otherwise, the calculator is simply wrong.
It's even consistent with a simple causal model. Obese people have larger bodies, which require more maintenance -- a larger supply of blood vessels and a heart working harder to fill them, more energy expended in getting up and going to the bathroom, et cetera. So it's kind of "no mystery."
Now, it might still be the case that this documentary was correct -- for example, while basal rates might be higher for obese people, perhaps normal-weight people simply have an exercise routine which increases their metabolism in general. Something like that would be useful and would help colomon understand why the result is backwards. Unfortunately, I didn't see the documentary and therefore I don't know this particular reason, but the question is legitimate and is not well-dismissed simply by saying, "oh you know that crazy internet."
The Katch-McArdle and Cunningham try to be more specific and relate to the Lean Body Mass (LBM).
However -- since LBM is reasonably correlated with overall weight -- then we can assume that (all else being equal) the fatter person has a higher BMR.
For example, suppose it assumes you'll have 15% body fat at your goal weight. If you told it your goal weight was 290 as opposed to 190, it would factor in 85 addition pounds of lean body mass and recommend extra calories to sustain that lean body mass. The article says something different: that the same person lean at 190 will gain less weight from an extra 10 calories per day than the same person obese at 290.
Both sorts of calculators are based on broad averages and simplifying assumptions. It's not like the people at about.com went out and carefully measured intake, metabolism, and weight loss for 10,000 people, making sure to have enough data to get statistical resolution between a 300-pound builder and a 300-pound couch potato.
