How about abandoning someone who needs me.
Why are you thinking of abandoning them?
I'm tired of his constant begging for help.
This person may be truly in a desperate situation with no one else to turn to. If you abandon them now and they end up in very bad shape later, you may end up regretting it.
How's it my responsibility if they were too stupid to get into this situation in the first place?
Of course it's not your responsibility but it's not nice to ignore if   someone in desperate need of help. How would you feel if you were in their place?  I'd suggest you to help them in any possible way.