Compared to varieties, vector bundles and derived categories on stacks are less understood. (Bridgeland) stability conditions are effective to study these objects, however in general they are difficult to construct. In this talk we construct tilt stability conditions on root stacks over smooth surfaces, and show their deformation dimension is at least as the even rational Chen-Ruan cohomology. I will recall the structure of derived categories of root stacks and the notion of Chen-Ruan cohomology. Then I will show the ideas of proof via 2 key examples. We will also discuss some potential further questions and applications.