I agree with John Poco.  The down force on the tail must be counteracted
by additional lift over and above the weight of the airplane.

Imagine you are flying level, and a passenger moves from the back to the
front.  To remain level, additional down force is required from the
tail.  This results in a slight increase in AOA and an increase in lift
equal to the additional down force on the tail.

Bob Belshe
N19BJ