This will probably be a challenging class for several of us, because we are being challenged to finish that project that's been sitting around forever or yarn that has been sitting in our stash about as long as we can remember.
Since each person's definition of a weed is different, there is no right or wrong project for this class. The story you create around it is what will make the difference.
The professor encourages us to use WIPs for this class, which means they would like to have a picture of the project prior to you starting up again on it to show the comparison. Find that shawl, those socks, that blanket that's been hiding forever. Check the thread for some specific projects that have already been approved or vetoed, such as previous House Cup projects that were never finished, with the exception being OWL projects that were never finished.
It has been stated that bonus points will be awarded based upon how epic or legendary these projects are in your family or knitting group. Extra bonus points if a testimonial is videotaped. Or if there is dust involved.
Now, if you don't have any WIPs or horrible yarn lying around, you could always go the literal route and knit weeds. Or maybe pick a technique that you haven't attempted before that seems particularly daunting. Entrelac? Lace? Cables?