We have been legally separated since 11/12/13. He is living in the marital property, and we both pay half of all the expenses, as is written in the legal separation agreement. The home is in NC. He wants to move to PA with his girlfriend, and expects me to move back into the home and pay all expenses, with him paying nothing. The mortgage is in my name only, but he is on the deed. The house is for sale. Can he legally back out of the agreement and leave me to pay for everything?
No.
You should file for a divorce, attach your separation agreement and proceed forward. You have been separated more than a year. You should be able to get a divorce absolute.
If he refuses to pay his half, you can get court orders compelling him. If he leaves the state, those orders can be domesticated wherever he goes, causing him serious grief.
No - failing to abide by the agreement is considered "breach of contract" as a separation agreement is treated as a contract between the parties. However, as suggested in other answers, if you file for an absolute divorce (since you have been separated for a year), the separation agreement can be incorporated into the divorce decree, causing the agreement to become a court order. If he fails to abide be the agreement (now court order), you can seek to have the order enforced through the contempt powers of the court. I would consult with an attorney if he fails to follow your agreement to obtain assistance in enforcing your agreement, as well as obtaining an absolute divorce and incorporating your agreement into the divorce decree. Best of luck.