Your Analysis is flawed.
Comparing medal count performance by population is interesting, I'll give you that you that. And one can learn a lot from the data.
But measuring a countries overall Olympic performance based on population alone is not one of them.
Let's take Jamaica for instance. With a population of roughly 3 million they took home an astounding 11 Olympic medals. Look further and you will see that all those medals came from Track and field, look again and see that all the medals came in the sprints (400 and below).
By your logic we could assume that if Jamaica had a population of 6 million they could take home 22 Olympic medals double it again and the number goes to 44 Olympic medals. But the potential for 33 more medals in the sprints alone is just not there.
In order to keep up the same pace, Jamaica would have to start earning medals in different disciplines (distance, field events etc..)
Areas where they don't currently have the systems in place to train and get Jamaican athletes to compete at elite levels in these disciplines, not to mention the whole breadth of other summer sports which make up the Olympics.
For a country to maximize their potential at the Olympics, they need to have systems in place to train and allow athletes to develop in a wide variety of disciplines.
For example: It doesn't matter how big the U.S. population is, if they didn't have an education system that provided scholarships for athletes. Out of necessity, sports would take a back seat and you wouldn't see as many world class athletes.
Of note: Over time, a large number of athletes competing and winning medals for their respective countries all around the world have taken advantage of education/athletic training systems in the United States and other countries with similar opportunities.
Should the countries who created these opportunities to help develop these athletes get some credit for their medals? Just a thought...
The United States performance at the Olympic games is impressive by any standards. By the same token Great Britain's performance is as well.
Should the US take pride in their Olympic performance? Yes! It's quite a feat for a country to perform so well over such a large variety of disciplines.
It's short sighted to point to Population Adjusted data as a way demean US's achievements. Because that data clearly doesn't tell the whole story.