I do not like the idea of culture or having loads of population giving any increase to a sphere of influence.That is an unrealistic concept without any frame of reference or basis in reality.
I do not think it is completely out of line: I think the larger the population, the more space travel, trade, and space activity would occur. Now it would not be a direct proportion, and over time as the populations grows larger, the less the sphere would grow so by the time you reach a population of 20 billion, 40 billion would not influence the sphere all that much, if it all...
Now, am I space population expert... no, but I play one on cable TV...
Or in other words, I am just throwing an opinion at you!
Remember that the evil which is now in the world will become yet more powerful, and that it is not evil which conquers evil, but only love -- Olga Romanov.