負担:ふたん : a responsibility, usually financial, which is declared by a system. "If a guest falls off the hotel roof, it's the hotel's responsibility." "The parent is responsible for paying for the child's lunch at boarding school."

 背負う:せおう: an emotional burden, which is NOT part of a pre-arranged system: Taking care of your retarded sister, dealing with your son's alcoholism, the feeling that you let down everyone on your team.