I agree with everyone else. I know what you're thinking: "I cannot just throw away 2 years of my life!" but honestly, things are only going to get worse with time, especially as she becomes older and more dependent of him (heck, she may even use that as her excuse to move in with you and spread her grubby fingers, inserting herself into your relationship once again). The same will happen if you get married, heck, even if he moves out. She wants control and is not willing to give it up, nor is he willing to cut the umbilical cord. I would not be surprised if he feels he cannot move out because she guilt trips him every time he mentions it. Don't even think of having kids with this man, unless you enjoy being constantly told you're a bad mother and having her raise your kids at every opportunity she gets, convincing him that mommy is best at raising the baby.
The career thing is an excuse, in my opinion, because he would otherwise ask you if he can move in with you (I am confused about this though, since you say "We spent New Years Eve at his house" and also say "he went back home" as if you two live in different places, but then mention "we need to move out" We? So which is it?). Honestly, a man who wants to grow up and become independent will find a way. I have met middle-aged men who admittedly were not very successful in life, but they still moved out. How did they pay rent? They got a roommate or two, and split the rent. They will tell you in a heartbeat that they'd rather have a roommate than to live with their parents. In reality, the woman in his life is his mother, not you, she is his number one, so let her have him!
I very, very briefly dated a guy whose mother was in every aspect of his life. I got fed up within a month. He had to ask for her approval in EVERYTHING, including his circle of friends and who he dated. Divorced women and women with kids were unacceptable, under no circumstance was he allowed to date them, nor women who did not have a post-graduate school education, like he did, so I knew staying with him meant decades of drama, fighting, going against this crotchety old woman, and said no thank you. We are still the best of friends but I will not date him or have any sort of romantic relationship with him. He is 41 and she still manages his bank account, to give you an idea of her reach. He won't put her in her place because he thinks it will hurt her feelings -- and worries she will cut him out of his inheritance too if he does so. Then he wonders why he is a bachelor still and if that's his future. I have bluntly told him yes, you will be single for life, but he seems okay with it and won't change a thing. It is what it is.
No woman will put up with a man child, and that is why your boyfriend was also single until you scooped him up. Unless you don't mind being put in second place and having mommy take precedence over you, having him always defend her, and having him never stand up to her if she gets in between you or trash talks you, then you will see this relationship for what it is and cut your losses. It is time to find yourself a real man who has his own mind. I live alone and support myself and will gladly continue staying alone if the other alternative means taking up with a man-child like your boyfriend. I've already got a kid at home, I don't need two, or drama from an intrusive MIL, no sirree. It's up to you if you want a third wheel in your relationship for the rest of your life, or if you don't want to welcome drama and a scared little boy who is a mama's boy and trembles at the thought of going against her. Think about it and choose wisely.