The study of minimal degree varieties in projective space is a classical question in algebraic geometry.Nondegenerate varieties of minimal degree were classified by Bertini and Del Pezzo and exhibit several nice properties, for instance, they are generated by quadrics and have linear syzygies. Extending this theory to nondegenerate varieties in some weighted projective spaces, we'll discuss lower bounds on the degree of a nondegenerate weighted projective variety and some classes of weighted projective varieties attaining the bound.