you will need to create a separate shipping rule for each weight range using the Subtotal For Any Column.
for example:
Name: total weight more than 1001g but less then 1999g
Triggers:
"Subtotal For Any Column"
If the Subtotal of column "totalWeight" is ">=" a value of "1001"
AND "Subtotal For Any Column"
If the Subtotal of column "totalWeight" is "<=" a value of "1999"
Calculation:
Flat rate charge of "x"