Acoustic borehole images provide high-resolution borehole-wall structure, but large-scale interpretation remains difficult because dense expert annotations are rarely available and subsurface information is intrinsically multimodal. The challenge is developing weakly supervised methods combining two-dimensional image texture with depth-aligned one-dimensional well-logs. Here, we introduce a weakly supervised multimodal segmentation framework that refines threshold-guided pseudo-labels through learned models. This preserves the annotation-free character of classical thresholding and clustering workflows while extending them with denoising, confidence-aware pseudo-supervision, and physically structured fusion. We establish that threshold-guided learned refinement provides the most robust improvement over raw thresholding, denoised thresholding, and latent clustering baselines. Multimodal performance depends strongly on fusion strategy: direct concatenation provides limited gains, whereas depth-aware cross-attention, gated fusion, and confidence-aware modulation substantially improve agreement with the weak supervisory reference. The strongest model, confidence-gated depth-aware cross-attention (CG-DCA), consistently outperforms threshold-based, image-only, and earlier multimodal baselines. Targeted ablations show its advantage depends specifically on confidence-aware fusion and structured local depth interaction rather than model complexity alone. Cross-well analyses confirm this performance is broadly stable. These results establish a practical, scalable framework for annotation-free segmentation, showing multimodal improvement is maximized when auxiliary logs are incorporated selectively and depth-aware.