We establish new weighted Hardy-type inequalities involving the Diamond-alpha derivative within time scales calculus, unifying discrete and continuous settings. By introducing weight functions, we generalize classical Hardy-type inequalities and derive conditions ensuring the sharpness of the constants. The results extend known inequalities by providing optimal bounds and covering various time scales, such as real numbers, integers, and q-calculus. Applications to dynamic equations and illustrative examples are presented, demonstrating the interaction between weighted functions and dynamic derivatives. These findings deepen the understanding of weighted inequalities on time scales, offering new avenues for generalization and application.