Computer-aided Whole Slide Image (WSI) classification has the potential to enhance the accuracy and efficiency of clinical pathological diagnosis. It is commonly formulated as a Multiple Instance Learning (MIL) problem, where each WSI is treated as a bag and the small patches extracted from the WSI are considered instances within that bag. However, obtaining labels for a large number of bags is a costly and time-consuming process, particularly when utilizing existing WSIs for new classification tasks. This limitation renders most existing WSI classification methods ineffective. To address this issue, we propose a novel WSI classification problem setting, more aligned with clinical practice, termed Weakly Semi-supervised Whole slide image Classification (WSWC). In WSWC, a small number of bags are labeled, while a significant number of bags remain unlabeled. The MIL nature of the WSWC problem, coupled with the absence of patch labels, distinguishes it from typical semi-supervised image classification problems, making existing algorithms for natural images unsuitable for directly solving the WSWC problem. In this paper, we present a concise and efficient framework, named CroCo, to tackle the WSWC problem through two-level Cross Consistency supervision. CroCo comprises two heterogeneous classifier branches capable of performing both instance classification and bag classification. The fundamental idea is to establish cross-consistency supervision at both the bag-level and instance-level between the two branches during training. Extensive experiments conducted on four datasets demonstrate that CroCo achieves superior bag classification and instance classification performance compared to other comparative methods when limited WSIs with bag labels are available. To the best of our knowledge, this paper presents for the first time the WSWC problem and gives a successful resolution.