If the dates are presented as week numbers, then Spotfire sees the column as of type 'Date'. This means that you should be able to easily choose any of the 'date' presentation options. If you click on the weekly date column in your visualization (x-axis in your example), you should be able to see a 'flyout' triangle to the right of this column. If you click that triangle, you see lots of different presentation option, the first being the actual date value. If you select that option, the axis should display the actual (weekly) date, instead of the weeknumbers.
If this is not the case, then the week numbers must have been derived differently. You can then check if the week date column is indeed of type 'date' or perhaps of type 'string'. If it is not a date, you can use a transformation to change this column's type. Once that is done, you should be able to present the actual date values on the x-axis.
If nothing works, please share your dxp file. That makes it easier to have a look at the issue.