India was part of the 'non-aligned' block and at various times has been keen on building ties with the Russians, buying lots of arms from them. In contrast, Pakistani leaders have been firmly in the US camp. Hence, in '71 it was a no-brainer for Nixon which side the US would support. It is bizarre the Nixon continued supporting Pakistan during the Bangladesh Genocide, but that's Nixon for you.

Also, India did invade and annex Goa in '62.