With the emergence of large multimodal models, dual-encoder alignment via contrastive learning has seen a resurgence. However, the escalating model size demands effective Parameter-Efficient Fine-Tuning (PEFT). While LoRA is a promising inference-free alternative to adapters, we find that its naive application to multimodal tasks causes a severe rank imbalance, favoring the text modality and FFN layers. To address this, we propose HALoRA (Hierarchical Allocation LoRA), which introduces a component-wise budget allocator to ensure balanced fine-tuning across both modalities and their internal components. This is complemented by a gradient-approximated initialization to accelerate convergence. With only half the parameters of adapters, HALoRA achieves superior or competitive performance in retrieval and zero-shot classification. Our work presents a more principled approach to multimodal LoRA and uncovers an intriguing asymmetry in vision-language alignment, paving the way for future research. Code is made available.