How does marinating with sugar improve cherry tomatoes jam?
There could be a couple reasons for this:


Leaving the tomatoes in sugar allows them to macerate, which breaks down the cell walls and pulls water from the fruit, making them much softer.
If your recipe calls for pectin the sugar may be for gelling. Pectin needs sugar in order to gel properly, and the maceration probably introduces more sugar into the interior of the fruit than it would have normally.


If dietary restrictions prohibit the addition of sugar, it could probably be left out. If you do leave it out I would suggest replacing it with a non-sugar sweetener and a thickening agent besides pectin (or no sugar needed pectin).

However, if you are canning this and storing it for a long time I wouldn't recommend changing the recipe. Changing recipes that have been designed for canning and storage could lead to improper pH in the product and the development of botulism as it ages.