Accurate lymphoma segmentation in PET/CT images is important for evaluating Diffuse Large B-Cell Lymphoma (DLBCL) prognosis. As systemic multiple lymphomas, DLBCL lesions vary in number and size for different patients, which makes DLBCL labeling labor-intensive and time-consuming. To reduce the reliance on accurately labeled datasets, a weakly supervised deep learning method based on multi-scale feature similarity is proposed for automatic lymphoma segmentation. Weak labeling was performed by randomly dawning a small and salient lymphoma volume for the patient without accurate labels. A 3D V-Net is used as the backbone of the segmentation network and image features extracted in different convolutional layers are fused with the Atrous Spatial Pyramid Pooling (ASPP) module to generate multi-scale feature representations of input images. By imposing multi-scale feature consistency constraints on the predicted tumor regions as well as the labeled tumor regions, weakly labeled data can also be effectively used for network training. The cosine similarity, which has strong generalization, is exploited here to measure feature distances. The proposed method is evaluated with a PET/CT dataset of 147 lymphoma patients. Experimental results show that when using data, half of which have accurate labels and the other half have weak labels, the proposed method performed similarly to a fully supervised segmentation network and achieved an average Dice Similarity Coefficient (DSC) of 71.47%. The proposed method is able to reduce the requirement for expert annotations in deep learning-based lymphoma segmentation.