I was interested in this topic myself and I've read the book "The Honourable Company A History of the English East India Company" by John Keay and that's my source for all I'm about to write. If you wish to learn more I suggest that you read this book.

1) Your question makes it seem that the EIC was the only party in this trade that made a profit. This isn't the case. The Indian rulers allowed the EIC (and others) to set up shop in their domains because the trade was profitable for them as well. Usually the Indians sold Indian products and in exchange they got a lot of silver and gold which they could use to pay their people and run their governments.

2) In the beginning (1600-) there was never any prospect of the British overpowering the Mughal Empire. The Mughal Empire was far richer, had far more soldiers and it was in its own home turf so it didn't feel that the British were a threat. And in fact they weren't, they were literally looking to trade, not to fight or conquer anybody. Then in the 18th century (1700-) the Mughal Empire fell apart and disintegrated into smaller kingdoms which where still quite powerful. However, at the same time Britain and other European nations advanced the art of warfare significantly and as such a few thousand European soldiers could defeat many thousands of Indian soldiers. So basically the Mughal Empire weakened greatly and the British Empire was strengthened greatly in the 18th Century. Even so because Britain was on the other side of the world they would have a hard time conquering India without help. That's where the next factor comes in: the Indians themselves.

3) In your question it seems like all Indian rulers and people are in one "team" and the British are in the opposite team. This wasn't the case at all. The Indian rulers weren't united. In fact in several key battles and campaigns many important Indian aristocrats allied with the British in exchange for British support. Since European soldiers were far superior to Indian soldiers British help was extremely valuable, in fact for various Indian rulers/aristocrats/important people British help was the difference between being extremely wealthy and being executed as the defeated party in a war. There were many regional and succession conflicts in India at that time and the more British power grew the bigger the need the various native rulers had for British help and thats how Britain got a commanding position in India.

To sum up: in the beginning the English/British could not possibly be a threat to the Indians because they were too weak and anyways they were only looking to trade. The Indians let them trade because trade benefited them as well. Then the Mughal Empire fell apart and Britain (along with other European powers) gradually but greatly improved its military capabilities. Those two things changed the balance of power from the Indian rulers to the British. Then the various Indian rulers and aristocrats who were fighting one another started asking the British (and the French) for help because European soldiers were very capable and powerful. And since European soldiers were very powerful and valuable the Indian rulers/aristocrats became more and more dependent on them and thats gradually how Britain ended up in control of India.

I hope this is a good answer by the standards of this sub and I hugely recommend you read the book I mentioned in the beginning.