How do mountains form, and why do they stop growing?

Mostly through tectonic collision thickening the crust, and they stop growing because erosion and gravity eventually balance uplift — so a mountain range's height reflects an equilibrium rather than an accumulation.

The main formation mechanisms:

Continental collision. Two continental plates converge, and because both are buoyant neither subducts readily, so the crust thickens and buckles. The Himalayas are the active example, formed by India colliding with Asia and still rising.

Subduction-related. An oceanic plate descends beneath a continent, generating magma that rises to build volcanic ranges, with compression thickening the crust alongside. The Andes are the standard example.

Fault-block mountains, where crustal extension causes blocks to drop and others to stand high.

Volcanic construction, building mountains from erupted material.

Isostasy — the concept that explains their behaviour. The crust floats on the denser mantle, like a block of wood in water. A thick block floats higher and also extends deeper. Mountain ranges therefore have crustal roots extending far below them, and the visible height is a fraction of the total thickness.

This is why they stop growing. Several processes converge:

Erosion removes material from the top, and rates increase sharply with elevation and relief — steeper, higher, wetter terrain erodes faster.

Isostatic rebound. As mass is removed, the range floats upward, partially replacing what was lost. So erosion lowers the surface far more slowly than the volume removed implies — a range can lose enormous quantities of rock and lose comparatively little height.

Gravitational collapse. Crust cannot support unlimited thickness; beyond a point it spreads laterally under its own weight.

Glacial limitation. Above the snowline, glaciers erode extremely efficiently, and the glacial buzzsaw hypothesis proposes this effectively caps mountain height in glaciated regions.

When uplift stops entirely, erosion and rebound continue for a very long time. Old ranges such as the Appalachians and the Scottish Highlands were once comparable to the Himalayas, and their present modest height is the result of hundreds of millions of years of this process.