When we’re inside an aeroplane, when we’re in cruise, why is it that we don’t feel the changes in altitude, lift and the adjustments for example from the elevator on the plane as the weight is burned in cruise?
When the airplane's weight is reduced, as fuel is burned, the pitch attitude (angle of attack) and required thrust necessary to maintain the desired speed are also reduced.
This happens very slowly and the adjustments in pitch and power are so small that the changes are essentially imperceptible.
People can feel even small changes in acceleration if they happen quickly, but slow changes in acceleration would need to be very large to be perceived at all. While adjustments in flight parameters to deal with changing fuel load wouldn't affect acceleration, a plane in altitude-hold mode would nonetheless have a certain amount of undulating motion, and the perceptually smoothest autopilot algorithms would likely have larger variations in acceleration than an autopilot that was designed to minimize such variations.
Focusing on horizontal acceleration because it's a bit easier to reason about, imagine that one had a ball hanging on a 1m string from the ceiling of a plane that was accelerating forward with an acceleration of 0.01g. That ball would seek equilibrium point that was about 1cm away from vertical. If the plane's acceleration were to instantly drop to zero, the equilibrium point of the ball would instantaneously change by 1cm, and the ball would swing noticeably with a period of about two seconds and a peak speed of well over a centimeter per second.
If instead the plane started with an acceleration of 0.02g, but reduced its acceleration gradually over a period of a minute, the ball's initial displacement would be about twice as big as in the earlier example, but it would take a minute to reach vertical, and its maximum horizontal speed would be an order of magnitude below that of the earlier example.
The human vestibular system is a bit more complicated than a hanging ball on a string, but similar principles apply.
Part of the answer is that even violent control surface action is not felt if the result is level flight. While you may have significant changes in the vertical airspeed, corresponding to significantly changing lift forces (for example in order to counteract up- or downdrafts), ideally the airplane experiences little change in vertical ground speed: It stays level in space and is not accelerated much. In fact, maintaining level flight was the very reason for the control surface action.
The same is true for the adjustments due to the weight loss from expelled fuel. Ideally, the reduced lift forces stay equal to the reduced gravitational forces so that the result is zero vertical acceleration and hence level flight (except perhaps minor, slow attitude changes). The cabin is not accelerated so that nothing is felt.