What is the vertical load limit for a 2 X 6 wall?

How about 3 tons? Sorry but, your question is terrible. It doesn't portray your ability to build anything. I'm not even an engineer nor possibly able to answer further. You seem concerned and are asking for a specific reason, but then provide nothing:

- Wall height or width

- Exterior sheathing or not

- Lateral blocking or not

- Single or double top plate

- Number of doors or windows

- Load spread-out or localized

- Pine or Douglas Fir structure

- Snow, Wind, Roof material load

- Number of stories