Forest fires are serious disasters that affect countries all over the world. With the progress of image processing, numerous image-based surveillance systems for fires have been installed in forests. The rapid and accurate detection and grading of fire smoke can provide useful information, which helps humans to quickly control and reduce forest losses. Currently, convolutional neural networks (CNN) have yielded excellent performance in image recognition. Previous studies mostly paid attention to CNN-based image classification for fire detection. However, the research of CNN-based region detection and grading of fire is extremely scarce due to a challenging task which locates and segments fire regions using image-level annotations instead of inaccessible pixel-level labels. This paper presents a novel collaborative region detection and grading framework for fire smoke using a weakly supervised fine segmentation and a lightweight Faster R-CNN. The multi-task framework can simultaneously implement the early-stage alarm, region detection, classification, and grading of fire smoke. To provide an accurate segmentation on image-level, we propose the weakly supervised fine segmentation method, which consists of a segmentation network and a decision network. We aggregate image-level information, instead of expensive pixel-level labels, from all training images into the segmentation network, which simultaneously locates and segments fire smoke regions. To train the segmentation network using only image-level annotations, we propose a two-stage weakly supervised learning strategy, in which a novel weakly supervised loss is proposed to roughly detect the region of fire smoke, and a new region-refining segmentation algorithm is further used to accurately identify this region. The decision network incorporating a residual spatial attention module is utilized to predict the category of forest fire smoke. To reduce the complexity of the Faster R-CNN, we first introduced a knowledge distillation technique to compress the structure of this model. To grade forest fire smoke, we used a 3-input/1-output fuzzy system to evaluate the severity level. We evaluated the proposed approach using a developed fire smoke dataset, which included five different scenes varying by the fire smoke level. The proposed method exhibited competitive performance compared to state-of-the-art methods.