Why Newton's law of universal gravitation is a valid law? What causes any two bodies in the universe attract each other with a force? Why Newton's law of universal gravitation is a valid law? What causes any two bodies in the universe attract each other with a force? What causes a larger body in space to have a gravitational pull on a smaller body?
 A: 
Why Newton's law of universal gravitation is a valid law?

The empirical fact that bodies gravitate is the given.  Long before Newton's law of universal gravitation, bodies were gravitating because that's the way the universe is.
Physicists endeavour to describe observed phenomena with mathematical models that, if valid, give reasonable agreement with observations.
The question of why the observable universe, the given, is the way it is isn't really within the realm of physics and, in fact, may not be a valid question at all.
Indeed, if one were to give an alleged answer to why?, there is no reason to suspect that such an alleged answer would be immune from the question "but why is that so?"
A: There's no point here like "Specific object pulls another specific object", everything interact with everything. (By the way, there's no specific conditions for these interactions.)
And why? At first, this law is some kind of conventionality, and we use it because of its simplicity. Then, a simple logic: if it works and helps us, why not use it?
A: Because any weight - it preserved the condition of many types of energy in the amount of potential energy components, i.e. Wpot / c ^ 2 = m. But potential energy, as is known, always tends to a minimum value and the maximum density, i.e. to minimum volume. Why? Probably because that was not so closely in the universe at speeds of hundreds of km / sec. This commitment to the minimum potential energy is called the gravity.
I'm sorry, I gave an answer to this question is still 14 May 2014 But I do not speak English and so the answer is written first in Russian, then placed the Google translation. 
A: This is about as meaningful a question as "why is $\pi \approx 3.14$", or "why is the speed of light the same in all reference frames". It just is, it's a law of nature.
A: Ali Abbasinasab,
Well, the simple answer is that physics just doesn't know why massive bodies attract each other. And not because your question is meaningless. Your question: "What causes a larger body in space to have a gravitational pull on a smaller body?" is actually the essence of physics, which asks: How things work? 
If somebody still doesn't like the word "why", it can easily by replaced with "how" here, so that we have: "How exactly a larger body gravitationally attracts a smaller body?"
[Paragraph added] Obviously it is just my opinion, so let me just quote Feynman from the video I just spotted in luksen's comment to the answer by Alfred Centauri. When answering the question of "Why two magnets attract each other?" he says: "Of course it is a reasonable question. It's an excellent question!" And later, after playing  with the idea of a rubber band (which he admits would be cheating), he says: "I'm not going to be able to tell you why magnets attract each other, except to tell you that they do."
So, back to gravity, physics is actually desperately looking for an answer here - hence the concept of the graviton for instance, hence the endeavors to unify General Relativity and Quantum Mechanics. Yet this question asked openly certainly is very inconvenient for contemporary physics. Because you are actually asking about transmitting the gravitational force. Which brings about the force at a distance concept - do we accept it or not? Because if one body pulls another body, than how is this physically (mechanically) done? And physics actually is (in very strange ways) trying to give the answer to this question with its theories of curved space or gravitons or gravity waves. But these answers still do not tell "why".
First of all, curvature itself cannot make a body move (toward another body or just toward a point). If curvature produces movement, it is only because there is gravitation underneath it. That's why a ball rolls down the slope. It takes curvature (of the ground) and also it takes gravitation under (the ground). If you remove the force and leave only the curvature ... nothing happens to the ball; it will stay right where it was. So curvature cannot replace gravitational pull, it cannot replace a real force. Physics is perfectly aware of that, and therefore still looking for the answer.
Concepts of graviton and gravitational waves are no better in giving the explanation. They are pretending to be the answer as to how the pulling force is transmitted, but they are still failing to do so. You can easily show how a (messenger) particle pushes another particle away, but you cannot show how it pulls it toward the "sender". Saying that virtual (admitted to be only mathematical) or real particle tells another particle (body) to move closer is ... funny, to say the least. The same pertains to a wave. Wave propagating from A to B can only push thing B away from thing A, and not pull it. So physics can easily explain how a force pushes things away from each other, but it cannot show how it pulls them towards each other. (Pluses and minuses as regards charge are also no explanations - physics doesn't really know how a minus attracts a plus. How a particle with a minus knows that out there is a particle with a plus, and why would it want to move?)
So, it's not that your question is "philosophical" or "metaphysical" or even nonsense. The thing is that physics has no mechanical answer to your question, it doesn't really know how the force is transmitted. Therefore it avoids it, because its "ashamed" (and says your question is "silly"). Because physics actually quit giving mechanical explanations nearly 100 years ago now, and now it concentrates on mathematical formulas. (That's why you will hear for instance that photon might have a spin, but then this spin cannot be "real" - nothing is allowed to be actually spinning). Physics still doesn't like the concept of force at a distance, and at the same time it doesn't like to admit it has no real clue as to how attracting (gravitational) force is conveyed.
Therefore you are said elsewhere that physics doesn't care about "why". It is said to only care about formulas. Well that's the way it works now, because from the time of Einstein, or perhaps even before him, physics has been taken over by mathematicians. That's why Feynman said: "Shut up and calculate!". But questions of the kind you asked are perfectly valid, and of utmost importance. Mathematicians do not care about understanding, physicists just the contrary.
As an epilogue, I want to quote ... Feynman again (6'30"): "I must say that it is possible, and I often made a hypothesis that physics ultimately will not require mathematical statement. That the machinery ultimately will be revealed ... It always bothers me that in spite of all this local business, what goes on in a tiny ... no matter how tiny a region of space, and no matter how tiny a region of time, according to laws as we understand it today, it takes a computing machine an infinite number of logical operations to figure out. Now, how can all that be going on in that tiny space? That, why should it take an infinite amount of logic to figure out what one stinky tiny bit of space-time is gonna do? And so I made a hypothesis often that the laws are going to turn out to be at the end simple, like the chequer board, with all its complexities apparent". 
Now my hypothesis is that if we really want the laws to turn out simple, we need to look for answers to the questions like "What causes any two bodies in the universe attract each other with a force?" And certainly, contemporary physics with all its piles of maths, and forbidding to inquire about the "how" is not trying to achieve that goal at all.
P.S. I am probably going to get quite a few downvotes for this answer, but this is the (sad) truth. I am, therefore, looking forward to real counter-arguments.
