Why do heavier objects provide more reaction force? According to Newton's third law, to each action there is an equal and opposite reaction, which means that no matter how heavy is the object, if I give it X amount of force, it will give that force back to me. However, if I were standing on top of a skateboard and I throw a bowling ball with X amount of force, it will push me to the back more than if I threw something really light like a golf ball with that same force. 
Why is that?
 A: Suppose we have an object of mass $m$.
You stand on a skateboard and throw that object as hard as you can.
Suppose your arm can put out a maximum force of $F_\text{max}$.
When you push the object with your maximum force, its acceleration is $a = F_\text{max}/m$.
The position of the object as a function of time during this acceleration is the usual
$$x = \frac{1}{2} a t^2 \, .$$
Your arm has only a certain length $L$ so you can only apply this force and get the object to experience that acceleration over a distance $L$.
Therefore, the maximum time over which you can push the object is
$$t = \sqrt{2L / a} \, .$$
The final momentum of the bowling ball is therefore
$$p = F_\text{max} t = F_\text{max} \sqrt{\frac{2L}{a}} = \sqrt{2 L F_\text{max} m} \, . $$
So you see, the amount of momentum you can impart to an object goes proportional with the square root of that object's mass, the force you can exert, and the length of your arm.
Newton's action-reaction law says that the force exerted by you on the ball is equal to the force exerted by the ball on you.
Note, of course, that these forces are exerted over equal amounts of time, so the thing that's really equal in the end is the momentum imparted onto you and the ball (in opposite directions).
Since we see that the momentum you can impart on the ball increases with increasing ball mass, then the momentum exerted on you also increases with increasing ball mass.
Intuitively, this is all just saying that when you throw a golf ball, it's so light that it leaves your hand before it's had a chance to push back on you very much.
A: Short intuitive answer: because they have more inertia, and therefore will less easily modify their trajectory under interaction. So the interactor (if lighter) will have endorse most of the trajectory or deformation change, which translates by "strong reaction".
A: What a great Fermi problem!  Consider a bowling ball of 16 pounds mass.  If you toss it directly away from you, horizontally, at a height of 1.2 m, such that it lands 2 m from the release point. If you exert same force profile (impulse) to a golf ball at the same initial height, the golf ball would take the same time to fall, but would have a horizontal velocity (and consequently, distance)  that scales like the square root of the ratio of masses (see @DanielSank s answer). The standard golf ball has a mass of about 1.6 ounces, (16 ounces per pound), the that scale factor is $\sqrt{160}= 12.6$. So you would have to throw the golf ball over 25 meters, not a trivial throw.
I believe you are underestimating what it takes to exert an equal force.
A: Newton's third law of motion, the action-reaction law, does not directly depend upon the mass of an object; it depends upon the force.
By Newton's second law of motion we have $\text{Force} = \delta \text{momentum}/\delta \text{time}$, and momentum is the product of the mass and velocity; thus a measure of force is the change in $mass \times velocity$ per unit of time; this idealizes as $F=dp/dt$.
If the mass is unchanged by the action, then $F=\text{mass} \ \times \ \text{acceleration}=ma$, so mass enters into the reaction force. You can obtain the same force with different masses: if the mass is doubled, only 1/2 the acceleration is required, but if the mass is halved, you must double the acceleration.
By including the distance over which the force is applied, you bring up the question of work performed, which is a separate question.
A: Despite your best intent to use the same force in both cases, you push the bowling ball harder than you push the golf ball.  You may perceive that your force is the same in both cases, but it isn't.  You're using a lot of upward force just to hold the bowling ball, and it's very hard to give it just a little horizontal force.
Also, it takes more time to release the bowling ball than the golf ball, so the impulse is greater even if the force is the same.  It's the impulse that determines your backward momentum after the interaction.
