There was a long running thread on this subject about ten years ago. Can't find it at the moment.
On a naturally stable a/c, which is every large civilian type I can think of, the horizontal stabilizer has a cambered lower surface. Usually, completely flat on top. That suggests to me that in all flying conditions the stab is designed to create a downward force to balance a c of g forward of the c of p.
It is also notable that on a trimmable stabilizer the range of movement is far greater leading edge down than leading edge up.
Which also suggests that a downward force is almost always the requirement.
Storing fuel aft, either tip tanks in a swept wing or stabiliser (horizontal or vertical) is just a very efficient way of reducing the required stabiliser incidence in cruise and therefore reducing drag.
Storing fuel in the tips also aides wing bending relief but thats another topic.