This is a hard question because you will find sources that claim that calories from protein have less effect on body weight gain when compared to the same amount of calories from carbs or fats. Likewise you will find other sources that state that a calorie is a calorie regardless of its origin and hence consuming 2000 calories of protein would have the same effect on body weight when compared to consuming 1200 of carbs, 500 of fat and 300 of protein for example.
A proposed mechanism for protein calories having less effect on body weight gain is "thermogenesis" or in order words that some of the energy from protein calories is lost when processed by metabolic pathways after consumption, but this is not globally accepted by the scientific community. Here is an article from the International Journal of Obesity that discusses the subject. I would suggest being VERY picky with the references you find on the subject since there is a lot of info floating around in the web in sites without any scientific backbone.
Something that can be assured though is that different calorie proportions origin-wise cause different results for other variables different from weight such as body composition. In addition to this, there are several studies adressing the apparent statistical find that protein rich foods increase satiety and hence facilitate body weight control; however, the latter is not related to calorie intake count but rather to other factors that decrease hunger physiologically or psycologically.