How to sum measure value for all records between two dimension values
First you need two cube-dimensions because you cannot use one dimension on more than one axe of a MDX-select. You can use role-playing dimensions, that means there is only one "Week" dimension in the database but it is used twice with different names for the cube.

Second each Week dimension has to be connected to a measure group. If you use only one measure group with one column "WeekId" you can only get a measure not null when you select the same week from both dimensions.

One solution is to create a facts-table with the cartesian product of all combinations Week1Id, Week2Id and a value precalculated to the sum you wanted.

Or you use two measure groups, one for "FromWeek", one for "ToWeek" and store a rolling sum of the metric, here in one table:

Week  SumFrom   SumTo
1       0         6
2       6        11
3      11        15
4      15        18
5      18        20


and create a calculated 

MEMBER [measures].[result] AS ([ToWeek].CurrentMember, [Measures].[SumTo]) - ([FromWeek].CurrentMember, [Measures].[SumFrom])