In these selections from The Second Treatise Locke says something which it is critically important to understand. It comes in paragraph 54.
Naturally, all men are created equal. And yet they are unequal in talents and character, alliances and family bonds. These differences may make it reasonable for us to hold certain people in higher regard than others, and they are not the basis of moral equality, the equality under moral judgment amongst all men. This equality is like equality under the law, but here the law is the moral law, rather than political law. The respect in which we are morally equal is that every man has a right to be free and not subjected to another's will.
No one is to receive arbitrarily special favor or disfavor when he is judged by others. This is because no one has less or more right to liberty, the right to be left to act unmolested by others (except insofar as his prior violations of others' similar rights have made it appropriate to sanction his behavior.) This is the sense of equality underlying political equality under the law.
There is no trace here of equality as equality in character or talent - these Locke explicitly denies - or equality in desert of wealth. These are simply not there. Equality in desert of wealth is incompatible with the property rights Locke propounds in the treatise because redistribution of wealth in order to spread it evenly must violate these rights.
(An aside: Some libertarians have maintained that this is a violation of liberty, as well, such that to be the victim of redistribution of wealth is to be at least partially enslaved. I disagree with this. I think that violation of property rights is theft and not enslavement, since to have one's wealth stripped away is not to be forced to act or restrained from acting. Plunder is not enslavement. In any event, the salient point is that Locke distinguishes these types of equality and it is crucial to understanding our political system that one understand its basis in moral equality.)
(Another aside: One might notice two senses of "moral equality" here: equality in moral character and equality under the moral law. The latter holds amongst all people. The former is very rare.)
(A final aside: One might wonder what the grounds for equality under the moral law itself are. Here one might appeal to the meanings of moral terms and to human nature. Moral language embodies a conceptual system in which it is nonsensical to allow arbitrary differences in judgment where descriptions of events are the same and only personal identities differ; for more on this see the archives of Philosoblog. Also, human nature is such that the right to act without being subjected is innate. I think this basis in human nature may be reduced to conceptual facts about moral language, but that issue takes us far afield.)
