In verse two, "bear one another's burdens", the word translated "burdens" comes from a Greek word, "baros", which denotes a weight that places a demand on one's resources to the extent of being burdensome or unbearable.
In verse six, "his own load", the word translated "load" or "burden" comes from a Greek word, "phortion", which means something to be borne, like a soldier's backpack. Moffat translate this verse: "For everyone will have to bear his own load of responsibility."
"Burdens" in verse two would signify those life emergencies or crises for which we are incapable of dealing without the assistance of someone else. We are rightly enjoined to come to aid of another in those circumstances. That constitutes a healthy inter-dependency.
However, "burden" or "load" in verse five signifies those things which are our unique responsibility. When we try to get someone else to assume the responsibility for our "phortion", or when someone tries to pass off their "phortion" to us, that is co-dependency.