I`m wondering if the gravitational pull from earth that should be constant around the planet, will get amplified by a celestial body like the moon orbiting the earth?
Gravity itself cannot be amplified but the forces are additive. The earth is held in orbit by the Sun's gravity but earth is also affected by the moon's gravity. Depending on their position the moon's gravity could be aligned with Sun's gravity, increasing the gravitational pull. Or the moon could reduce the effect of suns gravity if on opposite side of the earth relative to the sun.