In response to the OP's question, I think the basic answer is that the abundance of light nuclei is determined by big-bang nucleosynthesis, which occurred at high temperatures. At those temperatures, there was a tendency for deuterium to break up. In comparison, helium is doubly magic
http://en.wikipedia.org/wiki/Magic_number_(physics) , so it's extremely stable, and any helium that formed in big bang nucleosynthesis was likely to hold together.
Another point to note is that although there are reactions in stars that destroy deuterium, there are none that create it. Therefore the abundance of deuterium in our universe is like a ticking clock that started counting down after the big bang. The fact that its abundance isn't zero is actually very strong evidence for the finite age of the universe. If the universe was infinitely old, then there would be no deuterium left.
tenchotomic said:
Then the question arises "why is it so weakly bound?"Does this has something to do with charge/mass ratio of the nucleus?
No, electromagnetic interactions are irrelevant to the stability of light nuclei. When you have a set of Z protons interacting, the number of interactions is Z(Z-1)/2, i.e., it basically grows like Z^2. In a heavy nucleus like uranium, with Z=92, electrical repulsion is a major player, but not for small Z. For Z=1 the Coulomb energy vanishes, which would tend to make the nucleus *more* stable.
For light nuclei, the most stable ratio of Z/A is 1/2. This isn't because the protons are charged. It's because of the Pauli exclusion principle, which favors equal numbers of protons and neutrons. Again, this should actually favor the stability of deuterium.
A couple of generic reasons why we should expect deuterium to be unstable:
(1) Nuclei are most bound in the region around iron. Nuclei lighter and heavier than iron are less bound, which is why you can generate energy by fusion of light nuclei and fission of heavy nuclei.
(2) Odd-odd nuclei are always unstable compared to odd and even-even nuclei.
What's actually quite surprising is that deuterium is *stable* with respect to beta decay. Almost all odd-odd nuclei are unstable.