Cooperative perception allows connected vehicles and roadside infrastructure to share sensor observations, creating a fused scene representation beyond the capability of any single platform. However, most cooperative 3D object detectors use a uniform fusion strategy for all object classes, which limits their ability to handle the different geometric structures and point-sampling patterns of small and large objects. This problem is further reinforced by narrow evaluation protocols that often emphasize a single dominant class or only a few cooperation settings, leaving robust multi-class detection across diverse vehicle-to-everything interactions insufficiently explored. To address this gap, we propose a class-adaptive cooperative perception architecture for multi-class 3D object detection from LiDAR data. The model integrates four components: multi-scale window attention with learned scale routing for spatially adaptive feature extraction, a class-specific fusion module that separates small and large objects into attentive fusion pathways, bird's-eye-view enhancement through parallel dilated convolution and channel recalibration for richer contextual representation, and class-balanced objective weighting to reduce bias toward frequent categories. Experiments on the V2X-Real benchmark cover vehicle-centric, infrastructure-centric, vehicle-to-vehicle, infrastructure-to-infrastructure, and vehicle-to-infrastructure settings under identical backbone and training configurations. The proposed method consistently improves mean detection performance over strong intermediate-fusion baselines, with the largest gains on trucks, clear improvements on pedestrians, and competitive results on cars. These results show that aligning feature extraction and fusion with class-dependent geometry and point density leads to more balanced cooperative perception in realistic vehicle-to-everything deployments.