Hi,
If all the products have the same shipping cost, you can set a weight of 1kg for all your products and then create manual shipping methods for each increment:
from 0 to 1.5 kg => 6.5
from 1.5 to 2.5 kg => 13
..etc..
If the products need to have different shipping costs, that's not possible.
You would have to build your own custom shipping plugin to handle that.