You make a good point about the US having empire elements in the 19th century but was the US considered among the "great powers" by the Europeans of that time?
If in 1880 a European colonial power wanted to take an island let's say in the Caribbean or South America would they have been wary of US power and backed off?
Well, the Spanish-American war showed that the US had burgeoning military as well as industrial and commercial strength when they inflicted a string of heavy defeats on Spain and took most of its empire in the Caribbean. The Royal Navy also defacto enforced the Monroe doctrine so yes, most European powers were cautious about meddling in the Americas.
America's role in multinational events outside of Europe such as the Boxer rebellion (as a major member of the Eight-Nation Alliance) showed that by the latter part of the 19th century the US was indeed a Great Power whose influence was substantial on world affairs. Obviously since they were the only Great Power at the time outside of Europe (possibly excepting Japan at the very end of the century) their actual influence on European events was substantially less then countries like Britain, France or Prussia, but on the world stage its power and influence were definitely enough to make a European Power wary of crossing it.
As to Britain specifically, America was a pretty natural ally because, unlike the other European powers, the goals of the US generally didn't conflict with their imperial goals. This combined with the rapid expansion and industrialization of the US in the 19th century made them ideal trade partners which further diminished a potential rivalry (at least in terms of one that would lead to military conflict, commercial rivalries between companies certainly existed). To a lesser extent this held true between the US and the other European Powers (as they didn't really have the kind of merchant fleets the UK did to really take advantage of transatlantic trade), in that the US was never really an existential threat to any of them, the way the other European Powers were (eg. France/Austria vs. Prussia), thus they would be far less likely to want to be dragged into a major conflict with the US the 19th century. Remember that unlike the US, every European power has to take into account what their neighboring powers will do when they act, particularly the UK in this situation since to seize land in the Americas and provoke the US you would have to project a fleet across the Atlantic. Even the UK was keen to avoid a conflict with the US (see 1895 Venezuela crisis, Oregon boundary dispute, Maine boundary dispute) because any conflict with the US would hurt them economically, require distant projection of force and in the end gain them very little even if they were victorious (and arguably hurt them long term because of lost trade and investment opportunities, particularly for industrialization projects such as the building of American railways).