How are arches formed by weathering?

Weathering and erosion.

Sandstone formations are brought to the surface by the removal of overlying rock structures by erosion, or by uplift from not-fully-understood tectonic processes. As the sandstone nears the surface, cracks appear in the rock formation from pressure release as the weight of overlying rock is removed by erosion. In arid regions, freeze-thaw cycles will enlarge the existing cracks, and the wind will ablate the sandstone into narrow wall shaped structures. Eventually, a hole may appear through these wall shaped structures, and enlarge to form arches. In temperate areas, water plays the biggest role in arch formation, creation occurring where two sandstone overhangs form back-to-back, and their eroded undercuts finally merge into an opening that eventually forms an arch.