I've posted various parts of this on other occasions:
Eagle backmarks first began to appear around 1800, from American companies, as a mark of patriotism and particularly after the War of 1812. Almost immediately, but especially after the war, British manufacturers began copying it, replacing previously used marks such as crowns and Prince of Wales plumes.
Quality descriptions such as “Treble Plated” generally appeared during the earlier part of the 19th Century. Indented backmarks began to appear around 1810, and raised backmarks were then progressively phased out. They’re rarely seen after about 1840.
The eagle alone is not a reliable indicator of whether a button is British-made or American-made but, as a result of various embargos on trade followed by the War of 1812, almost no British buttons were exported to America between 1808 and 1816 (apart from a brief period in 1810). When trade resumed in 1816, buttons were exported to America in huge quantities and dumped on the market with an openly declared intention to wreck the fledgling American button industry. Most manufacturers had removed backmarks that identified their buttons as British to avoid them being rejected by those with lingering anti-British sentiments. The American eagle became a surrogate method of side-stepping boycotts by patriotic Americans and increasing acceptance in the American market. Sometimes this was on the initiative of the British maker, and sometimes at the request of the American importer. This practice continued until at least the 1820s.