I'm not Indian, but I used to do this a lot when I was younger. My thought process was that a single dot would come across as serious or passive-aggressive (there's a discussion about this phenomenon somewhere in this thread) and ellipses would similarly be rude. Two dots somehow seemed like a nice way to come across as more friendly, and/or indicate a tiny pause between sentences.
I used to do this in the times when we were separately charged for every text with our cellular service. I'd try to fit as many sentences as possible to each sent message. With the rise of internet based texting, it became unnecessary to use sentence separators, because I could just separate them by sending multiple messages (and not use any punctuation at the end of each sentence, which is the current accepted "friendly" way of communication).
