Objects will fall to the earth with an acceleration of 9.8 m/s2. It doesn’t really matter what size the object is or how much it weighs as long as we ignore air resistance. It does not matter how fast the object is moving along the earth’s surface. That is to say any motion in the x direction has no effect on the motion in the y direction.
Cannonballs show a parabolic motion because they have a speed in the x direction that propels them forward. Their speed in the y direction is counteracted by the pull of gravity. Eventually they stop moving up and move toward earth accelerating toward earth at 9.8 m/s2. Please play with the following demo and note that there is a optimum angle to get the maximum distance.