If your plane is climbing with increased airspeed and the incidence is set right it's probably just a little nose heavy ... regardless of the manual CG. For good reason manuals would prefer you error toward a nose heavy CG.
A stable plane is designed so that when it starts loosing airspeed the nose will drop a little and pick up airspeed. The down-force on the horizontal stabilized reduces with the decrease in airspeed and causes this to happen balancing at the CG.
If the CG is too far forward you are trimmed straight and level you are flying with excessive down-force in the horizontal stabilizer. As the airspeed increases this becomes greater and greater and causes the nose to climb. It is much better to have this, than too far aft CG.
Too far aft, the nose will drop with excessive speed but when you are flying slow the nose will start to climb, slowing the plane and causing the nose to climb even higher causing an imminent stall.
That is why it's better to be too nose heavy rather than too tail heavy.
So a healthy stable airplane will climb very slightly with increased speed, also very true with full sized aircraft. If it's climbing too much, move the CG aft a little. If it ever has a tendency to descend at higher speeds .. the CG is too far aft and will be unstable at low air speeds.