Say from Independence to 1840. I'm sure opinions must have differed across Europe, but what were some different attitudes about the new country, and how did they differ from place to place/class to class/etc.
You could say there was a lack of respect. It's part of the reason the War of 1812 erupts. Britain and its use of impressment on American naval vessels was one of the main reasons for the war. Britain simply did not respect its old colony's new sovereignty. And you are right in that opinions differed across Europe. The American Revolution would be the catalyst for the French Revolution, one of the most important events in history.
[Disclaimer: not a historian, just a fan. Feel free to take this with a grain of salt]