Isaac Newton's Second Law explains that the acceleration of an object is dependent upon two variables--the net force acting upon the object and the mass of the object. In running gravity is the net force acting against you, your muscles are what cause you to accelerate against the gravity. Your mass stays the same, but depending on the field of gravity you're in, your weight can change. If the gravity is stronger, you're heavier, if the gravity is weaker, then you're lighter. When you're lighter but exert the same amount of force, you will go faster.
Newton's Third Law states that forces act in pairs. For every action force, there is a reaction force. Newton's third law of motion is that for every action there is an opposite reaction. this means when you run every time your foot hits the ground the ground pushes back with equal and opposite force. It is this force that propels you forward.