The way I understand the statistics I read, one of the best and most humane ways to stabilize human population to prevent the growth that scares you is to improve prosperity and increase the world's access to energy.
The places in the world where population growth is still a real challenge are generally very poor and have little in the way of controllable power sources that can perform tasks that people in the developed world take for granted. In those places additional children are often assets rather than expensive investments. If a farmer has access to a plot of land, but no tractor and no ability to hire help, a big family might be the answer.
My advocacy for energy sufficiency is not an advocacy for unchecked growth, but I am fundamentally opposed to achieving stability through deprivation. It does not work and it is the source of a great deal of human suffering.
One other reason that I am such an atomic activist is that the overall material investment in nuclear energy facilities is far lower than what is required for any other kind of available energy source. The energy density contained in uranium, thorium and plutonium really allows us to achieve a far greater amount of available energy and power with a far lower mass requirement.
I carry a simulated commercial nuclear fuel pellet in my pocket almost all the time. I sometimes pull it out when I need inspiration - that tiny, 9 gram mass that is about the size of the tip of my pinkie represents the pellets that release as much heat as burning a ton of coal. That comparison is valid today - with our primitive, once through then out fuel cycle. As we improve fuel utilization the ultimate limit is that the pellet could replace as much as 20 tons of coal.
Near my home there is a pass through the mountains with a rail line near a hiking trail. I recently spent a few hours on that trail. During the first hour, three trains, each pulling more than 100 cars full of 100 tons of coal per car pass through on their way to power plants. At least some of that coal is likely to have come from what used to be a mountain before it was blown up in order to expose the coal seam.
If you are worried about carrying capacity, work with me to reduce and gradually eliminate the need for that kind of material waste.