lug means ‘to carry something very heavy’. For example, I lugged a small sofa up the stairs all by myself when I moved house. lug around means ‘to carry something very heavy with you… without a destination’. For example, ‘I lug around a bag full of heavy books every day’. lug comes from luggen - an old Swedish word that meant ‘to pull someone by the hair’! So it is interesting that the modern English word lug doesn’t have a violent nuance; it just sounds very heavy and difficult.
A: My back hurts!
B: Of course it does! You’ve been lugging around those stupid shopping bags. Here… let me help you.
Did you have to lug around a heavy schoolbag when you were a child?