air travel – Excess baggage in vistara(or another airline) + KLM?

I have a single ticket from Kolkata, India to Amsterdam. The first part consists of a domestic flight with Vistara from Kolkata to Delhi and the next is with KLM from Delhi to Amsterdam. I was told by Vistara officials that I’d have to check in my baggage again at Delhi airport due to immigration.
My question is whether I’d have to pay for excess baggage at both the airports or paying once at Kolkata would suffice? I tried to contact both the airlines regarding this but received no answers.