An established weeping willow can be problematic. Not only is it short-lived, it's messy and has an invasive root system. As a rule, tree roots larger than 2 inches in diameter should not be cut through. Willows regenerate roots readily, so they may not be as sensitive to root loss as some other types of trees. However, removal of a large root may also compromise the structural safety of the tree. Large roots act as structural support for the tree. (The smaller roots at the tip of the big one also take up water and nutrients.) Loss of a large support root could weaken the tree and make it more likely to blow over in a windstorm.