This study proposes a novel approach to using TV subtitles within a weakly supervised (WS) Automatic Speech Recognition (ASR) framework. Although TV subtitles are readily available, their imprecise alignment with corresponding audio limits their applicability as supervised targets for verbatim transcription. Rather than using subtitles as direct supervision signals, our method reimagines them as context-rich prompts. This design enables the model to handle discrepancies between spoken audio and subtitle text. Instead, generated pseudo transcripts become the primary targets, with subtitles acting as guiding cues for iterative refinement. To further enhance the process, we introduce a weighted attention mechanism that emphasizes relevant subtitle tokens during inference. Our experiments demonstrate significant improvements in transcription accuracy, highlighting the effectiveness of the proposed method in refining transcripts. These enhanced pseudo-labeled datasets provide high-quality foundational resources for training robust ASR systems.