He doesn't really want the sippy cup. He wants the comfort of knowing you will be there at his whim. I went through something similar right before my daughter turned one. I went to her pediatrician and she basically told me I had to do something sooner rather than later because after a certain age it becomes a battle of will, versus, battle of needs. She told me I had 3 options and one would work much sooner than the others. Option 1: Put said sippy cup in bed with water only. Could lead to a bad habit and really isn't necessary. Option 2: No-cry sleep solution: go in, do not give sippy, rub his back or whatever to get him settled, leave, come back, comfort some more, leave, keep repeating. Do not pick him up, do not talk. Option 3: cry it out.
Our pediatrician really seemed hesitant to recommend the "no-cry" method because she said I was so tired that I really needed to get this taken care of (I was a total wreck), and that method could take a few weeks-months. She said if I could tolerate a few nights of crying, it would take a week to 10 days--she was right.
We chose option 3 because I work full-time, and I was going out of my mind from sleep deprivation. It took us 3 days of about 45 minutes of crying but on the 4th night, she woke up once and whimpered for a minute or two and went back to sleep. She is now almost 15 months and sleeps through the night no problem.
There are a lot of moms and dads out there who would never allow their child to cry for an extended amount of time--and I was definitely one of them. Unfortunately, I was also beginning to resent my own child because I was only getting two or maybe three hours of sleep in intervals so it made being her mom, and being a full time worker very challenging. She never seemed to harbor anger or fear of bedtime, she was always her same old happy self in the morning. Now we're so much better off and I think I truly enjoy being a parent so much more!
You could make an appointment with your pediatrician and see what he/she recommends. There are a bunch of books out there. I'm sure others will have great advice too! I know how hard it is to be so exhausted, it will get better, but it might require some work.
Best wishes to you.