Help my relationship?

been with my bf 5 years now engaged things r great.. one argument we continuously have is that i keep falling asleep, i work all week do sleepovers at work (where i dont actually get much sleep) when im with him i feel so comfortable and relaxed and cosy, it doesnt matter whether its my fav film thats on or a new one i want to see i fall asleep, he reckons i dont actually love him ( i do more than anything!) or that maybe im cheating (im not!!) im just genuinely tierd please help, how can i prove it to him, i do try altho he doesnt think i do