What causes tail-down force?
The phenomenon is called trimming.

This is the process by which the pilot adjusts the lift at the tail surface to shift the center of pressure right above or below the center of gravity and removes any stick force so the airplane will keep this attitude unaided.

If the center of gravity (CG) is right above or below the aerodynamic center (AC), the aircraft's longitudinal static stability is indifferent. Move it forward and stability increases, move it further back and the plane becomes unstable. The aerodynamic center is where the angle-of-atttack-dependent lift forces act, and in an indifferent configuration the lift coefficient on wing and tail will be equal. Increasing stability thus means to reduce lift at the rear surface, and if a lot of stability is desired, lift at the rear surface will become negative.

When the airplane is hit by a gust (change in vertical wind speed), the angle of attack at both wing and tail will change by the same amount. Now it is important how much lift changes relative to the lift before the gust. If the lift coefficient on the wing is larger than on the tail, the same amount of angle of attack change will cause a relatively smaller change of lift on the wing than on the tail, and the center of pressure will move such that it causes a correcting pitch moment.

By selecting the proper center of gravity location, the pilot can adjust the level of stability he/she desires. To stay at the desired attitude in flight, he/she now has to move the incidence of the empennage (or the elevator deflection) to a point where any pitch moment disappears. The consequence is a downforce on the tail if that is what it needs to trim the aircraft with the given center of gravity location.