Basic theory of Hobbesian contractarianism
Hobbesian contractarianism holds that there is nothing inherently wrong with actions such as murder or stealing or telling lies. There are no "objective morals" in that sense. Morals are only what society decides they are. (We'll get to who this "society" is in a moment; it is an important distinguisher of Hobbesian contractarianism from Kantian contractarianism.) It is socially useful not to have other members of your society arbitrarily killing you or stealing from you or lying to you. It is to everybody's mutual benefit in the society to avoid murder and lying and stealing, so that people don't have to be constantly looking over their shoulders, protecting their property and distrusting the word of everybody else. And so, "society" agrees on a set of mutually useful standards of conduct. This is the social contract. Nothing is written down on paper, of course, but an understanding is reached by unspoken consensus.
The outcome of the social contract ultimately depends on the relative bargaining power of those in the society in question. As a matter of fact, the weak, the disabled, the poor, and so on, have less power in society than the strong, the healthy, the wealthy. If the strong take from the weak, what can the weak do about it? Nothing. They need not fear retaliation. And the strong have little to gain from cooperation with the weak, whereas they must respect the strength of other strong people who may significantly affect their interests.
This inequality of physical strength and matter-of-fact bargaining power means that there is no "problem" for the Hobbesian contractarianism if the social contract involves outright exploitation of the weak and vulnerable by the powerful. Even slavery or killing the disabled is not considered "wrong" under such a system. The strong "society" doesn't gain much from the disabled, and the disabled can't retaliate, so why keep them around? It might be more efficient simply to kill them. They have no inherent right to be treated as equals, or anything like that, because as a matter of fact they aren't equal in any important sense. The ONLY important sense of "equality", to the Hobbesian contractarian, is equality of bargaining power. What type of bargaining power? Ultimately, only physical strength, wealth and influence count in this equation. If you don't have them, you're fair game for those who do.
By nature, Hobbesians argue that everybody is entitled to "bargain" to the full extent of their ability. What they call "moral constraints" are really just restrictions that arise in the bargaining process between parties that are roughly equivalent in bargaining power. And such moral constraints can only arise when bargaining power is equal. Thus, the Hobbesians conclude that no particular moral duties are owed to the weak or powerless, except insofar as other "strong" people demand them (by their own whim or fancy or whatever).
Criticism of Hobbesian contractarianism
How does Hobbesian contractarianism stack up against other theories of morality, such as consequentialism or Kantian ethics? Not very well. Why? Because Hobbesian contractarianism does not fit our common-sense understanding of what it means to be moral.
Many people, knowing nothing of abstract philosophy, feel that there is some kind of moral duty to help the needy, to protect the weak and vulnerable, to respect the intrinsic value of other people as people. They would say that while it may be advantageous for the strong to enslave the weak, for example, the weak have a prior moral claim to justice. They would applaud as particularly moral an act such as helping somebody when you stand to gain nothing or even to lose something yourself. The Hobbesian would think that there is little point in such altruism; there is no rational motivation for it. (Note: this doesn't mean a powerful Hobbesian contractarian won't ever help the vulnerable. But if he does do that, there will invariably be something in it for him, such as the admiration he gets from others of equal strength.)
In short, most people would say that there is more to living a moral life than seeking selfish advantage, even if seeking that advantage should happen to be "mutual" among members of a high-bargaining-power "society" that excludes the weak and powerless.
The problem, of course, is that you can't refute Hobbesian contractarianism as a moral theory by arguing for things such as the intrinsic value of all living things, or the duty to give equal consideration to all humans (let alone non-human animals). Why? Because the Hobbesian just doesn't believe in things like intrinsic value or equal consideration. Nothing you say will convince such a person that it is good to help the weak or powerless. The Hobbesian only believes in the good of helping oneself or those who can advantage oneself.
In conclusion, since Hobbesian contractarianism denies that there is a real difference between right and wrong that all people must respect, it is not really a moral theory at all. Rather, it is a proposed alternative to "morality", as it is commonly understood. It may lead to justice and equality where people have equal bargaining power. But it will almost inevitably lead to exploitation of the weak and vulnerable, because there is nothing inherent in the theory that values justice for all over exploitation of some. If people act justly in some circumstances, it is only because they are forced to settle for the "morality" of the social contract negotiated by the powerful. If they had irresistable personal power, the very idea of morality would be unnecessary.