J.,
This is a very hard thing to do. Wean them from nursing. On top of that, you have done the very same thing that many other (mostly first time) mom's have done, and that is have them sleep in your bed. I made the same mistake as well with the first, however the second one went straight to the crib, and was a much better sleeper and satisfied baby. I think we put them in our beds for OUR comfort, because we love them so much and it's a great time to snuggle, but at 16 months, they should also have their own space.
Anyway, the only way to wean him is to put him in his own bed. He sleeps with you, he smells the milk, he wants that comfort of sucking, and he wants to nurse. By putting him in his crib, it would alleviate a lot of that, and you will probably find that he's a much better night sleeper without the distraction. He may wake up in the middle of the night the first few nights to want to nurse, I know I had to stand outside their door and listen to them cry, and it broke my heart but in the end it was MUCH better for them, and they are really not crying because they need something, just because they're mad.
You will never break him of the night feedings if you don't take him out of your bed. And trying to do that, is almost like torturing him, since he's there in the bed with you, he smells it, and so he wants it.
By putting him in his own bed, you can talk to him about him being a big boy, about not needing to nurse, (he's drinking from a cup for goodness sakes) and he's going to sleep in his own bed like other big boys do. Have the conversation, explain it to him, so that when he does wake up crying in the night, you can re-emphasize it and he's not just feeling like you're taking it away, but there's an explaination that goes with it. He might start to understand better that way. Otherwise you're just taking it away and YOU know why, but he doesn't and therefore he just keeps crying until he gets it.
Ok, no words of wisdom I'm afraid, just what I have done in the past. We all do it. We all put them in our beds, and then it's so hard to get them out! However, it doesn't mean you're a bad mom, or that you love them any less, and you're actually not doing them any favors by continuing to baby them, and they WILL sleep better having their own space. We selfishly want them in our bed, but the best thing for the babies and their sleep, is to put them in their own bed most of the time, and make snuggling a special time, or once in a while he sleeps with you.
Good luck!