At the time of American Independence, both India and Caribbean sugar interests were more important economically to Brits than the US. Perspectives change over time.
One point of conflict was that the Crown would not let the colonists settle west of the Appalachians. I guess they wanted to forestall any more Indian wars.
If the Americans had ever persuaded the government to relent on that point, I guess they would have run up against Louisiana eventually.
Of course, if the Brits had wanted to, they could have taken Louisiana. Not since the time of Joan of Arc have they ever fought a war with the French and lost it.