There most likely would be no American Revolution. How long would America remain under British rule. What would be the fate of the Native Americans. What about immigration, sports, and America's canal system. Would slavery end early and about relations would better or worst than OTL.
What would be the worldwide effects? No or later Latin American Wars of Independence, the Napoleonic Wars, India, and later colonization of africa.
You may wish to search this board for American Revolution threads, as there has been a lot of discussion in this broader area. That way, you can read up on other people's thoughts and ask more specific things that regulars might want to talk about a bit more.
If enough concessions were given to the Americans and there isn't excessive interference in American affairs, its likely the American colonies would stay part of the world empire Britain would creating. Gradually these domains would get given more and more autonomy. Either a very loose federal system would occur, or they would gradually get given complete independence, in a manner similar to Australia and Canada in our timeline.
Personally, I feel the Albany Plan of Union is extremely unlikely to happen. While I feel there is a decent chance of some compromise occuring, I can't see Parliament allowing such a powerful single assembly to compete with it. More likely is greater autonomy to individual states or groups of states.
General consensus on the board seems to be that Native Americans may do slightly better, but there would be no sea change, as white settlers on the ground would want their land regardless of the governance system. Preventing this would be extremely hard to enforce.
Immigration is likely to be more from the British isles, although some would still come from other countries. Modern sports happened a long time after this, but would likely be similar in both geographies. America's canal system is likely to be delayed.
Slavery is a difficult question. It's possible that the slave trade would be ended a few years later, but outright abolition is likely to happen by the early 1830s when the franchise is extended in Britain. (I can't see the Great Reform Act taking longer - it's likely to come sooner if anything.) This is likely to cause severe protest from Southern states and the Caribbean, with a lobby in parliament, but they would be mad to go to war with their northern neighbours, the world's most powerful navy, and the vast bulk of their export market at the same time.
Consensus seems to be that some form of the French Revolution is going to happen, but it was such a chaotic event Napoleon's rule is likely butterflied away. Who knows what would come instead. As the Latin American wars of independence occurred partially due to inspiration from the US and from the destruction of the Spanish fleet during the Napoleonic wars, they are likely to happen a lot later.
British dominance in India would likely happen the same way, as the stage had already been set for this during the Seven Year's War. The scramble for Africa happened so much after your point of divergence, it would be very hard to predict, and there are many plausible scenarios. Lots would be affected by how European history unfolds.
