the stores admin section will only show the original shipping options that are supported by power store, it will not show any new shipping options that you add after the fact.
you will need to define new shipping rules for each of the weight ranges, for example, for the first one:
triggers:
Sub Total For any Column -
If the subtotal of column 'weight' is '>' a value of '0'
AND
Sub Total For any Column -
If the subtotal of column 'weight' is '<=' a value of '100'
Charge:
flat rate of 1.39
you will need to create other shipping rules for each of the other wight breaks.