He's not abusing the social system by getting child support from you. That's how it is supposed to work.
Sorry but as a child of an absent parent - get out of her life for good unless you want to develop a genuine relationship for reasons beyond reducing your CS payments, which it doesn't really sound like.
Give her the chance to recover from rejection and maybe someone will come into her life who wants to be a mum to her.
I'm forever thankful my bio father decided to f**k off entirely instead of flit in and out of my life.
If you do want to, I strongly suggest counselling for you.
I'm sorry for the circumstances which put you in this position but ultimately you do have a child now and it actually makes my heart hurt hearing that she tries hard to make you like her
That's not a burden a child should have to bear.