Hell, that's part of what being a social animal is all about. You take care of your weak, period.
Err.... Not exactly. See, inbetween the stages of "psudo-animalistic tribes" and "modern day" in human history, people were not exactly good to the weak, and even really are not so today. Modern thought encourages that we care for those unable to care for themselves, but it isn't really as ingrained as you claim. Being a social animal means working together to obtain the best compromise of a goal that could never be done alone. This sometimes will involve dropping a bridge on the weakist of your group. On the whole, most people don't really
like destroying the few for the good of the group, but it is a simple thing to rationalize. Technological and Philosophical advancements have allowed us, in the past few centuries, to begin moving away from this horrible part of what it is to be a society. Nonetheless, it's a work-in-progress.
And then there are just those that are so filled with hatred, fanatical madness, or just plain insanity that the weak will end up falling prey to them. Once again, we are attemting to move away from this by the use of prisons and mental health institutions, instead of the oft-used "drag to edge of settlement, pelt with stones untill dead" method that has so far been dominant in human history.
But back to the topic: The main issue here is that we have no real way to determine between those who need honest healthcare that they are trying to obtain but have no chance of getting, and dregs of society that wish to either do nothing or become a parasitic to the first person who will support them. Although such distinctions can eventualy be made easly, healthcare presents a problem in that it needs any particular patient's problem to be either solved or turned away
fast. There just isn't any solution that I can see here.