Although both walls do actually carry weight from above, there is normally only one of those walls which is truly the load bearing wall. This will be the wall which has:
-the overlap of ceiling joist ends on top of it in the attic if it is stick built, not truss.
- the load beam or footing wall below it in the carawlspace, or
- if it's a 2nd floor hall, usually only ine of those walls has a wall directly below it on the first floor. Same principal also applies for 1st floor hall over a basement.
This is standard for traditional western framing, the most common framing method in use today and for roughly the past 60 years. There are some variations from this, but this is generally what you will find.