We explore the dynamics of interacting phase oscillators in the generalized Kuramoto model with frequency-weighted couplings. We investigate the interplay of frequency distribution and network topology on the nature of transition to synchrony. We explore the impact of heterogenety in the network topology and the frequency distribution. Our analysis includes unimodal distributions (Gaussian, truncated Gaussian, and uniform) and bimodal frequency distributions. We observe for a unimodal Gaussian distribution, that the competition between topological hubs with dynamical hubs hinders the transition to synchrony in scale-free network, but eventually the explosive synchronization happens. However, in the absence of the very large frequencies, there is a gradual transition to synchrony, while if the frequencies are uniformly distributed the system shows explosive synchronization. When the frequencies are taken from a bimodal distribution, for a narrow distribution, a two-step transition occurs. In this case, central frequencies dominated the dynamics, overshadowing the topological features of the network. However, with Wider distributions, scale-free network exhibits a gradual increases in the order parameter, while in the fully connected networks a first-order transition happens. These results specifically elucidate the conditions under which two-step and explosive synchronization occur in frequency-weighted Kuramoto models, offering new insights into managing synchronization phenomena in complex networks like power grids, neural systems, and social systems.