The visual dubbing task aims to generate mouth movements synchronized with the driving audio, which has seen significant progress in recent years. However, two critical deficiencies hinder their wide application: (1) Audio-only driving paradigms inadequately capture speaker-specific lip habits, which fail to generate lip movements similar to the target avatar; (2) Conventional blind-inpainting approaches frequently produce visual artifacts when handling obstructions (e.g., microphones, hands), limiting practical deployment. In this paper, we propose StableDub, a novel and concise framework integrating lip-habit-aware modeling with occlusion-robust synthesis. Specifically, building upon the Stable-Diffusion backbone, we develop a lip-habit-modulated mechanism that jointly models phonemic audio-visual synchronization and speaker-specific orofacial dynamics. To achieve plausible lip geometries and object appearances under occlusion, we introduce the occlusion-aware training strategy by explicitly exposing the occlusion objects to the inpainting process. By incorporating the proposed designs, the model eliminates the necessity for cost-intensive priors in previous methods, thereby exhibiting superior training efficiency on the computationally intensive diffusion-based backbone. To further optimize training efficiency from the perspective of model architecture, we introduce a hybrid Mamba-Transformer architecture, which demonstrates the enhanced applicability in low-resource research scenarios. Extensive experimental results demonstrate that StableDub achieves superior performance in lip habit resemblance and occlusion robustness. Our method also surpasses other methods in audio-lip sync, video quality, and resolution consistency. We expand the applicability of visual dubbing methods from comprehensive aspects, and demo videos can be found at https://stabledub.github.io.