First, you have to very careful of the labels you use. These days we tend to stick labels on problems. Once such label is "Bully". Now Bullying is a real thing, and I don't mean to say it isn't. But we have expanded the label "bully" to include many things that it did not traditionally contain. As such we are very quick to stick the "bully" label onto a situation. 

The reason I say be careful with that is that being bullied requires you to be the victim. And in a mild situation like this (again, historically this wouldn't even fall under the label) you get to choose how much this impacts your life, both right now and going forward.  If you decide that this is the worst thing that has ever happened in your life, then it probably will be. If you decide that he is just annoying, then that's really all that will come of it. You get to decide where on the spectrum this falls for you. 

Another important bit of information. The most hurtful things people say to us are the ones that we are self-conscience about. Like it or not, if you're not secure in your appearance, then you will always seem to find people that pick on your appearance. That won't stop after high school or college. The only real ways to get it to stop are to be more secure in your self or to never interact with people. 

All that said, you are being annoyed, and you want that annoyance to stop. There is very little you can do practically. Going to the teacher may be the "correct" thing to do, but it won't actually fix the situation. You could try responding in kind, but someone that is out to cause you harm in the way you describe is probably not respecting you enough to like your words affect them (more on this in a moment). You might be able to switch classes or groups or whatever if you push hard enough, but that won't likely actually fix anything.

There are a few things you can do. One of my favorite things to say is "You can't control what others do, only what your reaction is." If this guy is giving you a hard time, simply decide that he isn't worth getting worked up over. It's very hard for words from someone you don't respect or care about to actually affect you. If you don't think that will work, then try looking at him and figuring out why he says those things. Does he have a bad home life or some other issue? Remember that. It's also very hard for words from someone you pity to hurt you. And finally. if he is still bothering you, look to the future. What and who do you think he will be in 10 years? Who will you be? Again it's pretty hard for words to bother you if you realize that the person saying them is pretty much at their peak and it's all downhill from here. 

As a last resort, internally, pick on him back. Don't vocalize it just keep it in your mind. When he calls you fat, remind your self he was "so desperate he wanted to date the fat chick". Or when he calls you ugly, remind your self that he is so stunted emotionally that he doesn't even know what ugly is. 

The last piece of advice is to take care if your self. Every time he calls you fat or ugly or whatever remind your self of someone that thinks your not. It can be tricky because we have a tendency to disregard the comments by people that love us while putting so much weight on those that dislike us. I tell my wife she is beautiful, and she tells me I have to say that because I am her husband. Even though there have been several occasions that I tell her honestly that such clothes don't look good on her, or he hair looks odd done up a certain way, etc etc (my point being that I don't just flat out always say she looks good, I am also critical too). My "wow you look amazing tonight?" get disregarded as a husband's responsibility, but let a patient at her job make her feel ugly and it has so much pull. Point being, think of the people that make you feel good when he is making you feel bad. A kind of "Well you think I'm ugly, but my boyfriend seems to enjoy me." can really soften the blow.