Earlier quoted context omitted.
Your base assumption seems to be that world influence has a positive linear relationship with population size, which is not something that I agree with. I don't necessarily disagree with it either, though. I think the situation is far more complex to boil down to just that.
I would amend that to say the potential for world economic influence has a positive linear relationship with population size. Clearly population alone doesn't do it, since China doesn't yet have the economic weight of the U.S., but they have a much greater capacity for growth.
It is possible that they are actually so large that it will start working against them. Like an animal so large that it can't eat enough food to stay alive.
I am certainly looking forward to seeing what happens, though. It's a very interesting time to be alive and I hope that China does keep growing enough to provide all of it's citizens with a quality life. They've made great strides in the past half century, in spite of their current government's many flaws.