Using the wrong setting on a clothes dryer can cause certain fabrics to shrink. People that are gaining weight would often blame the dryer for shrinking their clothes rather than take some personal responsibility. Hence the joke is they thought it was the dryer shrinking their clothes but it was them overeating aka the refrigerator's fault.
I could see Norm making a joke similar to this, but Id imagine he'd add onto the end by saying something after a pause, when the audience is visibly confused, like "Because I was getting fat. I was eating too much."