Does erosion make mountains become higher? Recently at the American Museum of Natural History in New York, I saw a display set that claimed erosion makes mountains rise higher, counterintuitively. The explanation was that the material removed from a mountain due to erosion makes it much lighter. Since the mountain sits on a landmass that is floating atop magma, a lighter landmass rises higher. (Similarly, boats rise higher in water when weight is removed from them.)

I have been looking for resources online to confirm this, but none mention it. They tend to claim that pressure due to shifting tectonic plates is the cause of mountain growth, and if they mention erosion at all, they only discuss it as a possible shrinking factor.

What do actual geologists have to say about this? Does it depend on the mountain range?
This actually does happen, a feedback loop between the Himalayas and the Indian monsoon. 

The Indian Plate is actively shoving itself under the Eurasian Plate, creating the Himalayas. 

At the same time, monsoon storms come up against the southern side of the Himalayas. The high mountains enhance the storms' rainfall, and the mountains erode much more on the southern side than the northern side.

Material is transported from the Eurasian Plate down onto the Indian Plate, and the weight removed from the mountains causes isostatic rebound of the Eurasian Plate, allowing the Indian plate to slide underneath, enhancing the uplift of the Himalayas., keeping the monsoon rainfall on their south side, etc. 

There's a more detailed explanation and some nice images here.