How it will work out is none of the Indian concern. It is the government of Sri Lanka and people of the Sri Lanka who decide what to do. In this case, Sri Lankan government believes that the military solution should be available when it is needed.
1. Sri Lanka is India's neighbour. Political developments there affect India. Therfore, it is of India's concern.
2. As I said earlier, India has a sizeable Tamil population who don't want to see India openly support the Sinhalese.
3. The question is not of 'bullying', but of foreign policy. If India wanted to bully Sri Lanka, she would stop funding the Sri Lankan army, stop supplying non-lethal equipment and stop bilateral trade. USA style.
In military terms, it is well needed in this situation... no military solution will make the government look like an idiot. Imagine Pakistan Army with no proper equipment to fight the terrorists. If you dont know.. that is whats going on.. Understanding that the situation in Sri Lanka is worst. Those guys a operating aircrafts to bomb military installations for god sake.. and India comes out to show sympathy for the terrorist, and denies the right of Sri Lankan government to procure arms is solely stupidity and uncalled for!
Sri Lanka is no angel in this. Its not simply a case of democracy versus terrorism. That's the world opinion anyways.
If it was, and If there were no Tamils in India, then perhaps India would openly support the Sinhalese, for the sake of stability.
However, considering the reality of the situation, India has no choice but to adopt a neutral stance.
Perhaps if China had been there instead of India, then there would have been Chinese troops taking out the LTTE with impunity.
Hell, if there had been China here, Sri lanka would perhaps not even exist as an Independent entity. But that's beside the point.
Here's a relevant link:
India eNews - India worried by Sri Lanka arms buying