Your question is made of two, so let's try to answer both.
- Why do some websites only allow you to see low resolution images?
This is, usually, due to two reasons, one is saving bandwith, a low resolution image uses less than a full resolution, so you can serve more pages more efficiently, and may be even cheaper. Then, some offer the high resolution one if you want to see it, this way, only people who really want to see that image, and most probably is really interested on the product will see, and then, the site is only expending resources on clients who are most probable potential buyers.
Second reason, is not stealing the image.
- Why do some websites only allow you to see a fragment of the image?
This is much less common than it should be.
A lot of times, products are identical to other similar ones, except for a small part, so showing you the whole image is not helping to see what is different, but showing you a close-up of the different part help to capture your interest and imagination. It may also be that the company is focusing the promotion on that specific area/aspect of the image, or the rest of the image is not really relevant for a first impression.
It also saves bandwith since they are already showing what people are interested on and only a few would like to see the whole picture.
Of course some times there are other reasons, it depends on the owner of the company, the designer, and all the people involved.