in the eCart object, go to the shipping tab.
you will need to create a shipping rule for each weight range, they will all be set up basicly the same, the only change will be the vlaues for weight and the flat rate charge.
for example the first one would look like:
Name "0 - 10KG"
Triggers:
Subtotal For any Column:
If the SubTotal for column 'TotalWeight' is ">" a value of "0"
AND
Subtotal For any Column:
If the SubTotal for column 'TotalWeight' is "<=" a value of "10"
Charges:
Flat Rate charge of "10"