Colon polyps in colonoscopy images exhibit significant differences in color, size, shape, appearance, and location, posing significant challenges to accurate polyp segmentation. In this paper, a Weighted Dual-branch Feature Fusion Network is proposed for Polyp Segmentation, named WDFF-Net, which adopts HarDNet68 as the backbone network. Firstly, a dual-branch feature fusion network architecture is constructed, which includes a shared feature extractor and two feature fusion branches, i.e. Progressive Feature Fusion (PFF) branch and Scale-aware Feature Fusion (SFF) branch. The branches fuse the deep features of multiple layers for different purposes and with different fusion ways. The PFF branch is to address the under-segmentation or over-segmentation problems of flat polyps with low-edge contrast by iteratively fusing the features from low, medium, and high layers. The SFF branch is to tackle the the problem of drastic variations in polyp size and shape, especially the missed segmentation problem for small polyps. These two branches are complementary and play different roles, in improving segmentation accuracy. Secondly, an Object-aware Attention Mechanism (OAM) is proposed to enhance the features of the target regions and suppress those of the background regions, to interfere with the segmentation performance. Thirdly, a weighted dual-branch the segmentation loss function is specifically designed, which dynamically assigns the weight factors of the loss functions for two branches to optimize their collaborative training. Experimental results on five public colon polyp datasets demonstrate that, the proposed WDFF-Net can achieve a superior segmentation performance with lower model complexity and faster inference speed, while maintaining good generalization ability.