So far I have come across three approaches:

1. Limit the space each weight takes to occupy in memory. The "quantization" you mentioned comes in this category. Tensorflow provides tools for doing post-training quantization: See https://www.tensorflow.org/lite/performance/post_training_quantization. An extreme case of quantization is using just +1/-1 as model weights. But this approach needs to you to train the model with quantization itself (AFAIK). Larq (https://larq.dev/) is an excellent library which use TF to train binary neural networks. You can also check latest paper from the same group which introduces a new Optimizer for binary neural network optimization. See https://papers.nips.cc/paper/8971-latent-weights-do-not-exist-rethinking-binarized-neural-network-optimization.

2. Delete the nodes (weights) which are not contributing actively to prediction (may be close to 0?). "The Lottery Ticket Hypothesis" (Article The Lottery Ticket Hypothesis: Training Pruned Neural Networks

3. Knowledge distillation. You first train a big network to the performance level you want and then train a smaller network by using the pretrained big network as it's teacher. Basically, you train the smaller network to mimic the big network predictions, rather than on actual labels. See Article Distilling the Knowledge in a Neural Network

You can test the Dropout and Bach normalization techniques. Moreover, if you want the best results, you should have more images in your Training Set, so you can add others ones of the same object when they existed if not you use the Data augmentation techniques.