This paper delves into the exploration of entropy in weighted graphs, where edge weights are determined by the Sombor Reduced Index. The primary aim is to establish and substantiate results by examining various graph types, including Connected Graphs, Star Graphs, Unicyclic Graphs, Regular Graphs, Complete Graphs, Complete Bipartite Graphs, Chemical Graphs, and Tree Graphs. Through rigorous analysis, we unveil the implications of these weighted structures on information content and structural complexities. Additionally, we extend our study to compute weighted entropies for molecular graphs representing specific dendrimer structures. This research contributes to a nuanced understanding of the informational intricacies embedded in diverse graph configurations, particularly emphasizing their significance in the molecular domain.