Newton-type solvers are widely used for solving nonlinear systems of algebraic equations, yet efficiently addressing complex systems remains challenging due to unbalanced nonlinearities. To overcome this, we propose a residual-driven adaptive strategy that dynamically balances nonlinearities by assigning adaptive weight multipliers to each component. These multipliers increase according to a specific update rule as residuals grow, allowing the solver to select optimal step lengths and ensure balanced reductions across all components. Importantly, this strategy introduces minimal computational overhead and seamlessly integrates with existing Newton-type solvers, enhancing their efficiency and robustness. Through extensive testing on benchmark problems, including a chemical equilibrium system, a convective diffusion problem, and challenging nonlinear systems, our algorithm demonstrates superior computational efficiency and robustness, especially in handling systems with highly imbalanced nonlinearities.