Acceleration is how quickly the velocity is changing whether it be speed, direction or both. Acceleration is a measure of how quickly the velocity of an object is changing.

Speed is how fast an object is moving in no given direction. Velocity is how fast an object is moving in a given direction. In physics, you can calculate the average speed by taking the total distance travelled and dividing it by the total time required to travel that distance.

Weight is the force acting on an object due to gravity. The weight of an object can be defined as the force of gravity on the object. Since the weight is a force, its unit is the Newton.