The main purpose of following a low sodium diet is not loosing weight, however it is well known that retaining less sodium in body definitely helps someone also retain less water. Therefore, people who cut on their salt intake tend to drink less water, hence keeping less weight.
The body tries to keep sodium in blood in a certain range. If you consume more sodium than your body needs, you will get it out of system through sweating, restroom visits, etc. The body will need more water (you will feel thirsty more often) to dilute the sodium content.
Considering that majority of the human body's weight is water, consuming less sodium is significant to being light!