As smokey_the_bear said, your basal metabolic rate will go up as you gain weight, meaning you will eventually need 3800 calories a day to maintain your current weight. I'm guessing this point is somewhere around 400lb, roughly. You'd have to add calories above and beyond to keep gaining weight.
Also you have to look at the level of activity. An athlete or construction worker can probably eat 3800 calories every day and not gain weight.
I know, I was doing it more to point out how sensationally stupid claiming the average American consumes 3800 calories is. The average American male weighs 190+lbs (IIRC) up 30lbs on 50 years.
My problem with calorific calculations, and even bodyweight averages in themselves is that they're so bogus. Post-war diets are vastly different than our current diets. The factors that effect body weight are also vastly different, I'm sorry but we've got thousands of medicines that weren't available 50 years ago, and one of the major contributing factors to weight loss is disease.
Americas weight problem isn't going to be resolved by figures and statistics, and it's certainly going to be hurt by poor statistics like those provided in the study in question.
How can a 190lb average American Joe consume 3800 calories working an Average sedentary job not be gaining a pound of body fat per week? The figures are ludicrously disjointed.
I understand that everybody is different, believe me I work in construction, I likely eat a thousand calories more than I'm recommended and I'm presently losing weight. My BMI says I'm going to drop dead, my vitals tell a different story. My heart is a near-perfect metronome when at rest (literally ~60 bpm), my body fat on my limbs is exceptionally low (especially my legs due to lots of moving heavy weights).
When I'm told I'm obese because of some voodoo astrology bodyweight index by a doctor who's showing all the signs of high blood pressure and could stand to lose a good 10 index points himself, I don't listen and in 20 years down the line I still won't be listening to the new doctor who's taken over the dead guys office because he'll be well on his way to rosy red cheeks and shortness of breath from picking up a tongue depressor.
Governments are paying for these studies that are providing sheer utter crap and they're trying to resolve weight issues by indirect action and instructing their overweight medical professionals to tell their patients to lose weight.
Here's my very simple solution: Vehicle free down towns nationwide. Not only will it be phenomenal for the environment (air quality, noise pollution, etc.) and provide a boon for public transit infrastructures, but it will also mean everyone is forced to get at least some exercise in during a work day.
Also you have to look at the level of activity. An athlete or construction worker can probably eat 3800 calories every day and not gain weight.