What process caused Virginia’s Blue Ridge Mountains to no longer be among the tallest mountains in the world?

A process that can change the size and shape of mountain ranges is weathering and erosion.  

Once among the tallest peaks in the world, the Blue Ridge Mountains of Virginia have been weathered and eroded down to their current size. Weather affects rocks. It may not seem like there is much friction between wind and rock, but there is a considerable amount. The same goes for rainfall that flows down rocky mountain sides. Those frictional forces, while not drastic, are present all of the time. Given enough time, weathering can greatly change the landscape. Freezes can create cracks within surfaces as well. That gives more surface area for weathering to work upon. As the surface is ground into smaller and smaller bits of sediment, erosion carries those materials away. After enough time, even mountain ranges no longer look the way they used to. 

In addition to the mechanical weathering discussed above, chemical weathering also plays a part. In chemical weathering, chemical reactions break down the bonds that hold rock together. That will cause them to fall apart and form increasingly smaller pieces. Common forms of chemical weathering are oxidation, hydrolysis, and carbonation.