I’ve never actually said anything about weight sharing. I was merely pointing out that unsupervised pre-training for classification is unnecessary, and that AEs can be trained end to end, rather than one layer at a time. This has nothing to do with weight sharing.
Regarding weight sharing, it might act as a regularizer, which could help when the model is overparametrized. For small models it could lead to underfitting. I don’t have an intuition how it affects the training process.
More importantly, I’m not sure if you can share weights when you use convolutional layers in encoder and decoder: could the same filters be used for both convolution and “deconvolution” purposes? Do you know any papers that did it?