Can I just check...
Is your Dad still wanting you to go and live with him?
Are you suggesting that you and your second cousin become a couple?
What does he expect you to do for your half-sister?
What decision does he expect you to make?
Sweetheart I have to say the same as I've been saying to you for years... You DESERVE to be HAPPY! Being overweight and having diagnosed illnesses do not make you less of a person. For your father to be bullying you about that is disgraceful and really should stop you from wanting to be anywhere near such an unkind man.
I've never, ever heard you sound anything like a monster. You are always kind and willing to do what is right for everyone else, but it's time you now put YOU first! Tell him how you feel. Start going out and meeting people - maybe join a group who have similar interests as you do - check local groups on Facebook etc. That could lead to more friendships, which could lead to more. Being in a couple isn't the be-all and end-all love. You will find the right person when you are not expecting to. Be kind to yourself!