1. Google had a huge advertising campaign to promote Chrome. It was unique and nothing like has been done for any other browser ever.
2. Majority of internet users in India are young. The mom's, dad's and grandmother's browser, I hypothesize, doesn't contribute as much to the stats as others. Many might have not even seen the pre-Chrome (or pre-Firefox) world.
3. Orkut was huge in India, Gmail and Google Search are bigger. Google has been pushing users to move to Chrome for a better experience for a long time now. That would have seen significant clickthrough especially because internet speeds have only recently started to pick up in India. Making the need for a 'better experience' more paramount.
4. Not enough business machines. Indian corporate world is not as highly computerized as North America or Europe. Indian Governmental Offices are way behind. While machines in western offices may bring about a significant increase in IE usage there, they will have lesser weight in India.
In Europe, Chrome has a small lead. In Asia, a medium lead. In South America, a large lead. In Africa, both are dwarfed by Firefox.
One possible unfounded speculation would be that it is connected to the age of the widespread adoption of the Internet. In North America, most users have likely been on the net for a long time and therefore use older, more established technology. In India, Internet access is likely a new thing to many people (and businesses), and they are therefore less "invested" in older programs.
Regarding your question on population, not sure how big is the Indian internet population. I would say 5% of the country(total pop. 1 bn approx) uses Internet regularly. Not sure how much that skews the data.
Could it be because it has to run on cheap hardware? Is there any more lightweight browser?
It might be better than IE in that regard, but it doesn't have any huge advantage over firefox.
Non-graphical: links, w3m. Other 'light' webkit shells: uzbl, Midori, Arora