When a body moves upward its own weight will act downward. We need some external force to move the body to upward because the weight acts downward.
The acceleration due to gravity acts towards the center of the earth or in other words acceleration due to gravity acts towards the ground.
In this case since the body moves upward and comes downward it will move under gravity or a free fall.
When a body moves upward the acceleration due to gravity will act downward. So this result in decreasing the rate of movement to upward. So to upward acceleration is negative.
At one stage the decrease in upward movement will result in stopping the movement. So the body stops and due to its own weight it will fell down. At this point the acceleration due to gravity will increase the rate of movement of the body because this time the body moves at the same direction of acceleration due to gravity. So the acceleration is positive.