Rights
To the root of the idea lies an assumption one has to accept: every man is equal. I don't mean in any pragmatic or specific way, just that no man's happiness and well-being should be more important than another's. Why should it be so? Well to be honest, I don't have much of an argumentation beside empirical and/or circumstantial historical evidence that most groups of people who ever tried to impose on others the fact that they had some kind of god-approved birthright had to eventually give most of it up or face a timely death like most monarchies did (French, Russian, Japanese, ...).That said, what is necessary to be happy? Well without elaborating on that specific subject, I will simply refer to Maslow's hierarchy of needs; one can argue about the structure, terminology or some choices, but the general ideas are there. Those are, in my opinion, the basic human rights and you will notice in Maslow's hierarchy of needs that nowhere are physical possessions mentioned. That's simply because possessions are completely irrelevant, they are either a mean to something you need or a replacement for something you need (this is probably a case of neurosis or something). Does that means possessions aren't a right, yes and no since, for example, you might have to stock some food for the winter so you feel safe you have enough to pass winter (not much of an example in today's world, but still), but anything over foreseeable (and reasonable) needs should be considered superfluous.
Responsibilities
Where does responsibilities fit in all this? Well, having rights doesn't mean they are owed to you if you cannot fulfill them yourself; it just means that one's action should never negatively interfere with another's rights, directly or indirectly, actively or passively; this is therefore our responsibility toward another: respect their own rights and help them to the limit of our capabilities, but never beyond it.Why should you help others if they cannot help themselves? Well if you have everything you need for yourself and have some to spare, but don't help, that would be admitting that you think your own happiness and comfort is more important than other's. Moreover isn't that what we instinctively do with our children? Cooperation is in our genes, it's something our whole world is built on and it is possibly one of our biggest edge compared to other species (see this TED Talk, the part specifically on cooperation starts in mid-video around 8 minutes).
Then why not helping other beyond our capability, sacrificing some of our "happiness" if it can make the life of another person much better, especially if a small sacrifice can make the other one much more happy (overall happiness level will be higher)? Well, this is probably where Mr. NiceGuy stopped and Mr. Pragmatic kicked in; this is the limit I felt needed to remedy the problem of the Free-Rider mentioned in the TED Talk above. Happiness is something hard to measure, so it could be easy for someone to claim that something would make him overly happier just to have it. Moreover, I think it might promote people not to fend for themselves, thinking that everything would be given to them no matter what; if people have already given all they can spare ... to bad for you you get nothing. It probably isn't the most "humane" way to go, but I feel a line must be drawn somewhere.