We feel the force needed to resist gravity, not gravity itself
Followup to david1300 - I have years of experience working in this field and know full well of what I speak here.
All objects with mass are acted upon by gravity such that they would experience a uniform acceleration in the absence of other forces. The concept of weight comes from the force needed to resist the acceleration that gravity would impart if left unchecked. In order for a mass to remain in an unaccelerated state relative to an earth based reference frame a force must be applied to that mass to oppose gravity. Remove that force and the mass will accelerate toward the earth at approximately 9.8 meters per second^2.
Force is measured between objects. In the case of an airplane and cargo, between the body of the aircraft and its contents. Because both the airplane and the cargo are subject to the same gravity field, the force between the two does not represent gravity. There cannot be any force between the airplane and its cargo without some external force acting on the airplane (and here gravity is not a force). On the ground at rest, the external force comes from the gear. In the air the external force comes from the engines and aerodynamic forces. In the air, the forces felt within an airplane have nothing to do with pitch or roll attitude. They are entirely dependent on thrust and the combination of angle of attack, sideslip angle, control surface positions, dynamic pressure (i.e., airspeed), and Mach number.
As the data provided by Machdiamond shows, the greatest X-axis acceleration occurs when thrust is high and during the rotation when the total lift is greater than 1g and along the stability axis such that some of it is experienced along the body X-axis. X-axis acceleration during a climb is roughly the same as during takeoff roll. It should also be noted that for transport aircraft with a thrust to weight ratio of 0.3 or less deceleration during landing rollout can result in an even higher X-axis acceleration in the opposite direction due to reverse thrust and braking.
This whole topic illustrates the criticality of pilots having a reliable visual reference for pitch and roll attitude as there is no means to determine those important airplane state parameters from the accelerations that the crew is experiencing.