So to answer the OP, yes welfare messes up natural selection but would we be better off without welfare state...that is impossible to answer, too many variables. Also we're very social beings, its in our nature to help each other. My very wild guess is, if there was no welfare state we'd kill each other as all the compassion would die out.
The OP has a point, if you look at natural selection on an individual level.
What if, you look at natural selection on a species level? In which, the species which for some reason, choose to allow those with "flaws" etc to reproduce. Those "flaws" may somehow enable the species to produce some individual (?hawking), which will elevate or somehow play some key role in the survival of the entire species.
We may be in the process of the natural selection of the entire race. If we display society traits, or otherwise, we may in effect remove our entire species from the selection process (nuclear war etc), and then another will come about and maybe they will not do the same.
So OP, it may be counter-intuitive to enable the "weak" to breed, but maybe this will be what saves the entire lot of us.