A pure weight-based test case generator for context-free grammars is introduced, where weights are set for each rule and used as unique driver to identify which one to apply during the derivation process; we demonstrate why static flat weights generally cannot work whereas, introducing a simple penalty mechanism, a dynamic weight-based approach is always able to produce random but finite sentences; then, looking at the source grammar from an original perspective, we proceed towards the definition of constraints through which, while still guaranteeing the convergence of the derivation, static but balanced weights can be identified: balanced weights own the interesting capability to drive the generation of an inexhaustible number of extremely random, structurally complex but finite sentences by an automatic test case generator having a dramatically simple derivation logic. Thereafter, we illustrate how to design a weight-based system which, by exploiting the characteristics of balanced weights, can be easily configured to produce sentences that address any specific coverage metric, including those not having a definite generative strategy yet. A complete example of the application of the balanced concept and the weight-based system is then included and experimental results are eventually shown.