As written:
String:  3 ** 2 ** 4
Weights: 2  9 2  9 2

##</code><code>##

String:   3 **  2 **  4
Weights: 20 80 20 81 20

More complex string:
String:   3 **  (   6   -   1   *   4  ) **  2
Weights: 20 80 90 120 140 120 170 120 90 81 20

String:   3 **  (   6   -   4  ) **  2
Weights: 20 80 90 120 140 120 90 81 20

String:   3 **  (   2  ) **  2
Weights: 20 80 90 120 90 81 20

String:   3 **  2 **  2
Weights: 20 80 20 81 20

String:   3 **  4 
Weights: 20 80 20 

String:  81 
Weights: 20