False equivalence.
1. Because of the civil war Tamil Nadu had to accommodate lakhs of refugees from Sri Lanka, a burden on the state's finances even today. Think of how the wave of East Pakistan's refugees to India in 1971 forced us to meddle in Pakistan's affairs and participate in a major war.
2. Many Tamils, especially in coastal districts have families in Sri Lanka who were affected by the genocide.
3. Spillover of the civil war/terrorism cost us our PM's life as well as many terror attacks, increasing crime, drugs etc. Sri Lanka wasn't the only party to the turbulent times.
4. LTTE fighters have sleeper cells in the state, some have joined Maoists as mercenaries, some have infiltrated the system etc. There is a lot of suffering, hurt and mindset of revenge which presents a security challenge for India since we are an immediate neighbour.
It is in India's and Tamil Nadu's interest to ensure that there is a logical conclusion to the saga and war crimes are addressed. Also legal help, Lankans have themselves requested our constitutional experts in this regard. Now that the mess has been created, we have been sucked in and no running away because we need to ensure peace in the region.
In this Khashgoggi case Indians and Pakistanis haven't been affected. Had our interests been affected we should have meddled. We literally have nothing to gain/lose in this issue, nor are we major global players indulged in power games in that region. In case of Sri Lanka we are the eminent South Asian power and have a say in what happens in our neighborhood.