The door weighs about 40-50 lbs and after you remove the door you have to turn around and lift it over the seats in front of you.
I actually went back and looked at my 737-3/500 saftey card to verify this. I didn't remember this requirement, but sure enough it's there.
What's interesting is that my Northwest A319 card shows the person tossing the plug door out of the plane. This is what I remembered, and was puzzled that the CO card has you throw it over the seats. Very confusing if you fly both airlines often.