Don't they learn to manipulate quick! :)
Yes absolutely stop the baba! At 2 years old he should only get 12 oz. of milk per day. He should also get fruits, vegetables, whole grains and protein. No more strawberry syrup!!!! That has more sugar then soda! That's why he's chubby, but not eating. He's drinking more calories then he needs, also why he's not hungry.
You've got to develop a thick skin. Kids know that they can scare you into giving them their way if they refuse to eat. Lets face it, we don't want to starve our kids. I'd start by giving him water to drink. You can add the milk to cereal, or mix into things like mashed potatoes or creamed soups. Keep his calorie intake in his foods, not his drinks. Its important to learn to drink water. Juice has a lot of sugar in it, even if its 100% juice. So eat the whole fruit and drink water, its much better for you! Our family does juice as a special treat, never regularly.
At 2 years old he's capable of understanding you, so let him know at meal times (3 per day) that he needs to eat what's on his plate. If he refuses, then don't give in to milk. He can have water if he's thirsty later on. No snack, just wait for the next meal. He might test you and refuse to eat for a day. Stay firm, if you give in its all over.
Also don't get guilted into feeding him mac and cheese, chicken nuggets, frys, pizza, burgers etc... He needs to eat REAL foods. A lunch idea is, some green beans (start with 2 beans, he HAS to eat them), a slice of tomato, mashed potatoes and a small amount of protein (meat, beans, egg, nuts, cheese, tofu). Or for breakfast, a few slices of fruit, small bowl of oatmeal, or cheerios (regular, not sugar encrusted) with milk, a spoonful of scrambled egg. If he eats it all, he can have more. If he eats what you'd consider a good size meal, reward him with a small cup of milk. Only give milk in a cup if he's eaten his food.
It might be slow going, but consistency is your friend here! He will learn to eat, he won't starve himself. We all have a few foods we don't care for, that's normal, but if they only have a few foods they like then there is a problem.
Best wishes!