A device is associated with a downhole tool to control the weight that can be set down on the tool while the tool is operating. A shroud is secured to the string that supports the tool with interior modular biasing components that for run in extend the tool past the shroud. Upon encountering a support for the tool, further set down weight compresses the biasing components for a predetermined stroke length delineated by the shroud landing on a support. If the tool is a mill, its operation takes place under the biasing force as the mill advances into the piece being cut or milled under a predetermined pressure. When the mill reaches full extension from the shroud the process can be repeated until the milling is complete. The shroud also centralizes the mill during milling.