I have read a lot of your comments - you post under the garb of the US flag but at heart you are a true "WE ALL KNOW WHAT". Anyhow, the point is simple - China realizes that without India on its side it will not be able to achieve supremacy in any world order - THAT is the POWER of the BIGGEST DEMOCRACY in the world!
2nd - India has already acknowledged the Chinese occupation of TIBET as LEGITIMATE.
3rd - No point taking India on right now as China has achieved much economically which it would not like to forgo in the near future. No point taking on an opponent who can inflict collateral damage to your nation thus pushing you back 20-30 years no matter what happens to the opponent. The cost of going back 20-30 years in the event of a war is way too big.
4th - There is only so much China can achieve funding certain nations. Quite clearly it has not yielded positive results in the past for I DONT KNOW HOW MANY YEARS. Trading with India is a better option than pouring millions into an outcome which is most likely not going to see fruition. They stand to gain BILLIONS without pouring any money into any nation.
5th - Further backing the biggest democracy is also an integration approach that the Chinese have been looking at and wanting from the rest of the world for many years - They stand to gain by changing their image as an opponent to democracy. If the biggest democracy is at ease with the Chinese then why not other democracies. IT IS WHAT YOU CALL PR.
I hope your doubts are cleared now.RIGHT NOW IT MAKES SENSE FOR THE CHINESE TO BACK INDIA!