As in OTL, in 1291 the first three cantons of Switzerland (Schwyz, Uri and Unterwalden) made an alliance directed against the Habsburgs. Since the Habsburgs didn't get Austria, Styria and Carinthia, they were much weaker, and also more concentrated on their lands in SW Germany. Very soon, in 1294, the Habsburgs tried to annex the Swiss Confederation, but were defeated at the battle of Morgarten, and the Roman king (who'd been in competition with the Meinhardiner in Tyrol, relatives of the Habsburgs) rather supported the Swiss. The fact that the Habsburg lands were divided after the death of Rudolf helped too. The confederation grew fast: 1310, Luzern and Zug joined the Swiss; 1334, Zürich, Glarus and Bern followed.
1354 the Swiss were strong enough to conquer the lands of the Rudolfine sideline of the Habsburgs, Aargau and Thurgau. The Habsburgs were angry, and the Roman emperor even was on their side this time, but when he died 1359, the Habsburgs had to fight alone and lost.
|List of Roman kings of the HRE|
|Nations that joined the HRE later: Poland | Prussia|
|Nations that left the HRE: Bohemia | Florence | Switzerland|
|Nations that became defunct|
An important development came 1375-78: The Süddeutscher Städtebund (South German league of cities) was formed. Various South German princes, led by those of Württemberg and Habsburg, fought them. With the help of the Swiss, the cities stayed victorious, and other than IOTL, their alliance wasn't interdicted by the Roman king. In this war, the Habsburgs lost most of their territories except Freiburg with the Black Forest. Now, the Swiss influence reached far north of the Rhine.
1456-69, the Swiss Civil War between "Upper Switzerland" (south of the Rhine) and "Lower Switzerland" took place.
During the Twenty-Year War, the Swiss used the opportunity and conquered the remaining lands of their archenemies, the Habsburgs, in the Black Forest.
1541-44, they fought and won the first Swiss-Savoy War, getting the control over Graubünden, Tessin and Veltlin.
Still, the country suffered from overpopulation; thus, it was welcome when in 1554 Braunschweig-Lüneburg formed its second province in Atlantis, and invited experienced woodcutters and sawmill builders there from Switzerland. After these immigrants, the colony was called Waldstätten (OTL Pennsylvanian Appalachians). And even despite of this emigration, ~1600 peasant uprisings happened here too.
1627-32, the second Swiss-Savoy War happened. At the beginning, the Swiss were in advantage, but later the rebellion in the Triple Monarchy of England-Castille-Portugal gave France the opportunity to strike against the Swiss. In the peace of Turin, the Swiss had to give the French-speaking area around Geneva, some fortresses in Alsace and at the Rhine (like Kehl) to France, and Savoy joined the Alliance des Alpes in return, becoming a French satellite. Even Switzerland itself was somehow dragged in the French net, and fought on its side in the Luxemburgian War of Succession 1660-64, making Vorarlberg a Swiss canton.
When France became a republic, at first many intellectuals in Switzerland were enjoyed about the development. But during the first French Republican War, French troops violated Swiss territory in the battle of Belfort. As a result, the Swiss Confederation now entered the war against France, and ended up on the losing side. Switzerland ceded its French-speaking areas to France in the peace of Brussels, but otherwise allied with France. As a reward, they received all of Württemberg in the peace of Basel 1784 following the second French Republican War.
1802, the first bigger anti-French uprising in a German state happened in Switzerland. Although the cities and plains could be brought under control, the more resilient population in the high mountains of the Alps and the Black Forest couldn't be stopped. The French reacted pragmatically this time, leaving the mountain people to themselves and have the Swiss government accept the loss of taxes.
The German Uprising of 1818 came so surprising that it didn't even spread to Switzerland; however, they managed to liberate themselves only a few years later, in 1824.