The shipping weight is most likely due to a package that’s big but light. Because it takes up a lot of real estate for it’s weight (low density) the freight companies charge based on an equivalent weight - what they would expect a package of that size to weigh. I forget the industry term for this but it’s basically a billing weight.
For example, if you were to ship a gigantic empty box, they would still charge you a lot even though the weight is very low.
The difference between 1300g and 1350g is 50g, or less than 2 ounces, or less than 1/8 lb. That could be the difference in the way somebody is rounding (it might be between 1300g and 1350g), maybe a difference in packing material, or maybe the 1300g ‘package box’ was put inside another 50g ‘shipping box.’