Complex neural networks require substantial memory to store a large number of synaptic weights. This work introduces WINGs (Automatic Weight Generator for Secure and Storage-Efficient Deep Learning Models), a novel framework that dynamically generates layer weights in a fully connected neural network (FC) and compresses the weights in convolutional neural networks (CNNs) during inference, significantly reducing memory requirements without sacrificing accuracy. WINGs framework uses principal component analysis (PCA) for dimensionality reduction and lightweight support vector regression (SVR) models to predict layer weights in the FC networks, removing the need for storing full-weight matrices and achieving substantial memory savings. It also preferentially compresses the weights in low-sensitivity layers of CNNs using PCA and SVR with sensitivity analysis. The sensitivity-aware design also offers an added level of security, as any bit-flip attack with weights in compressed layers has an amplified and readily detectable effect on accuracy. WINGs achieves 53x compression for the FC layers and 28x for AlexNet with MNIST dataset, and 18x for Alexnet with CIFAR-10 dataset with 1-2% accuracy loss. This significant reduction in memory results in higher throughput and lower energy for DNN inference, making it attractive for resource-constrained edge applications.