Does erosion make mountains become higher?
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.