Weight is a special column that is used for shipping calculations, so it is required to be just a number. If you want a text weight column I'd suggest adding it as another text column to the cart object, maybe named "size", and then it will allow you to put in anything you want.
Is the image getting inserted into the cart properly? If you view the source does it look like the image path you would expect? I can't tell by looking at your file if the problem is actually on the add to cart page and it doesn't store the image correctly, or if the problem is on the view cart page and the image path is wrong, but it would be one or the other. Try just displaying the name of the image in the cart to see if it was saved correctly in the first place.