Positron emission tomography (PET) reconstruction from low-dose to standard-dose acquisitions poses a significant challenge in medical imaging. While integrating Magnetic Resonance Imaging (MRI) for complementary guidance shows promise for enhancing reconstruction fidelity, current multi-modal approaches typically treat PET and MRI uniformly, neglecting their inherent asymmetry within the multi-modal context. This leads to insufficient utilization of anatomical guidance provided by MRI and neglects the unique metabolic characteristics of PET. To address these limitations, we propose MAK-GAN, a novel Generative Adversarial Network (GAN) that incorporates Multi-level Adaptive Kernels to distinguish feature extraction and interaction strategies between the primary (PET) and auxiliary (MRI) modalities in the asymmetric multi-modal PET reconstruction task. Specifically, we design a Multi-Kernel Extraction (MKE) block for both PET and MRI branches, replacing linear projections in vanilla Transformers with hierarchical multi-kernel convolutions. This enables efficient extraction of modality-specific features at multiple scales while reducing computational overhead. Subsequently, we asymmetrically introduce an Adaptive-Kernel Interaction (AKI) block in the PET branch. This block integrates self- and cross-attention modules to dynamically generate weights for adaptive kernels, preserving PET-specific characteristics while utilizing MRI’s anatomical information. Finally, we incorporate two PET-centric optimization strategies to prioritize PET during reconstruction: a residual connection for direct LPET-to-SPET mapping, and an edge-aware consistency loss to enforce structural coherence. Experiments demonstrate superiority on two PET/MRI datasets.