Our current research focuses on exploring the properties of entire and meromorphic functions with equal weights $l \geq 0$. We are particularly interested in understanding the unique characteristics of such functions by examining the general difference-differential polynomial $\Psi(z, f)$. This polynomial has been previously studied by \cite{hpv}, but our work builds upon their findings and provides new insights into the subject matter. Our study delves into the implications that arise when a polynomial of degree $n$ shares a common value with the general difference-differential polynomial. This is a crucial aspect of our research as it helps us better understand the relationship between polynomials and difference-differential equations. By gaining a deeper understanding of this relationship, we can contribute to the larger body of knowledge surrounding entire and meromorphic functions. These functions have numerous applications in a variety of fields, including engineering, physics, and computer science. In addition to our primary research focus, we have also posed an open problem for future research work. We believe that this problem has the potential to yield further insights into the behavior of entire and meromorphic functions with equal weights. Overall, our research seeks to advance our understanding of these functions and their applications, ultimately contributing to the broader scientific community's efforts to deepen our knowledge of complex mathematical systems.