Quote: Wellsy13 "I'd happily be corrected. I just don't see how a player's momentum is the reason why the ball goes forward, as if it was then surely the player's weight would affect the ball's forward motion as well (which it doesn't).'"
How technical do you want to get?
Nothing continues in motion without momentum, which is the sum of an object's mass and velocity. Prior to release the player and the ball comprise a single system with momentum comprised of their joint mass and velocity; at the moment of release a portion of that momentum is transferred to the ball as the player and ball become two separate systems each with their own momentum. The sum of the momentum of the ball and the momentum of the player equals the momentum of the two together at the moment of release. That's an approximation that works for real-life events at least - the pure physics gets complicated.
It's momentum that keeps the ball moving forward relative to the ground.