How does change in airspeed affect pitching moment?
How exactly do you plan to increase speed? You can add thrust. The aircraft is trimmed for a specific airspeed (normal flight assumed) so the added thrust will introduce a climb.

If you want to increase speed in level flight, you trim down (the engine power force vector rotating down, shrinking the vertical component and increasing the horizontal, so converting more engine power to forward movement and losing a little lift) AND add power to compensate for the lift loss.

It follows that there is an optimum: when there is no more vertical component, you cannot increase forward component of the engine force vector. But by that time the aircraft is already converted into a rock (no vertical force = only gravity = fall).