Given China's "one child" policy, it appears that their leaders are concerned that their population is too great. "Replacement rate" is 2.1 children per couple, so allowing just one child per couple (and without the great amount of immigration into Western countries) makes it appear that they intend for the future Chinese population to decline. I have read that the degree of environmental pollution, air and water, in China is such that decreasing the numbers of people (as well as utilizing more green technologies) is becoming important for future sustainability.
As for India, I have read that there continue to be governmental campaigns to increase family planning and to urge more men to get vasectomies. That would seem to indicate there is some concern there for population/population growth. Also, I have read that water scarcity and poor water quality are great concerns in India (If you want to know my sources, they include National Georgraphic magazine and NPR radio). Of course, I have not visited either country, as you have, but this is what I read/heard.
There are some concerns even in U.S., with just a quarter of the population in those two countries, with resource scarcity. Forty years ago, experts were expressing concerns that a large "Baby Boomer" population needed to pursue no more than 2 children per couple. The U.S. population during that time was approximately 200 million, and academics were projecting a severe population problem if Boomer couples had the 3-6 children their parents had. Now, 100 million more people later, I don't hear the same concerns expressed regarding US population size. The Boomers are now approaching old age and there is concern with having enough young workers to support them and man the economy (thus, the lax attitudes many have now toward immigration, including illegal immigration). The concern you hear more now in US is climate change, with droughts alternating with floods, depleting the fertility of the soil and the ability to grow crops (not to mention property/infrastructure destruction). Also, there is concern for water scarcity. The southeastern US has gained population as companies and jobs have moved from the industrial north to the south and west. Several southeastern US states now have concerns about having an adequate water supply. There is the same concern out west.
With clean water resources getting tight, and reduced fertility of crop lands, U.S. is facing a squeeze with "only" 300 million people to provide for. So, I'm guessing that having 4 times that many people, with often less than ideal land/resources to begin with, could really create concerns in India, China and some other countries.
Europe, on the other hand, has had a birth rate below replacement for years. Without immigration, that would become even more apparent. I do understand the concerns some have that the native populations and cultures in Europe could be supplanted in time by those of immigrants. I have the same concern in my own country.