Is it normal for my man to insist on me doing a polygraph?

I'm confused if I'm to stay with my man. I'm not sure if it is that I love him, or I'm too emotionally and mentally abused to know otherwise. He doesn't like the fact that I am fat. I've always been chubby, that's how he met me and pursued me, now he wants me to lose weight. He even said to me that my ex-boyfriend "really" left me because of my size. And that's not the case, he doesn't even know my ex. On top of all that he doesn't trust me. EVERYDAY day he insinuates that I'm being unfaithful, every guy he sees me talk to, or hear me talk about he says "jokingly" or asks "jokingly" how was the sex with them, but he uses the cruder version of the word "sex". I was usually a happy and bubbly person, but now...I feel so sad most times. I feel unattractive and I feel ugly. I feel down just to look at myself in the mirror. He wants me to do a polygraph and I have adamantly refused, and I will continue to refuse. I'm hoping that he will break up with me over my "defiance" as he calls it. I have tried NUMEROUS times to end it with him...but he just refuses to agree, so I'm hoping if I don't do the polygraph that will make him go. I've never cheated on anyone before, when I met him I had been single for almost 5 years, now when he accuses me of being unfaithful, in my head I say to myself "Why would anyone want me? I'm fat, they can do better". It's a hard struggle for me as I have to be going through this alone and in silence. I'm so happy I found this page just now. I feel so ashamed to let my friends and family know that I feel this way about myself, because I'm usually the happy confident one. But now I prefer to take solace in my room alone and cry, and replay his hurtful caustic words in my mind....