Have you ever thought about eating your garbage? How about grinding your garbage up into a puree and using the resultant glop to shampoo your hair?
The sun, the soil, and the rain have gone through a lot of trouble to create the weeds thrown away as garbage. In the recyclable world we live in it is a shame to let all that stored solar energy go to waste.
An interesting biological science project might be to catalog every garbage plant in your community, the nation and the world. Find out what is done with those garbage plants and what is the cost of disposal. Now find a use for most if not all the garbage plants on your list. Find uses for the useless.
In the beginning you can hope for some serendipity. Due to concerns about climate change, energy independence, and just the cost of living, scientists all over the world are turning to nature for alternative sources of food, fuel, and fiber. If you find, for instance, that scientists in New Zealand have found a use for an invasive plant species regarded as a pest in Zimbabwe then that counts as a success in your project. All you have to do there is to get the word out to farmers in Zimbabwe and anywhere else the plant is considered a pest that there may be an economical use for the plant and they should look into farming the weed and selling it at a profit.
Such mix and match activities will take care of all the low hanging fruit. The next stages are harder. What you will need to do is to find in your collection of weeds, plants that have been over looked or neglected. As for instance, let us suppose that a weed plant in Australia produces oily seeds. Do Google and library searches to find what kind of oil is produced from the seeds. If the oil or a near equivalent is being used elsewhere then you can recommend that research be done to render the oil useful. You will be like a prospector who goes out into the wilderness and finds something valuable that other people missed.
The final part of your project will be the hardest. Take things that insofar as you can tell are genuinely useless and find uses for them. It there was time and if you had the use of a laboratory then you could do things like perform chemical assays on seeds and leaves, grow cultures based on the plant extracts and test the plant extracts for their uses as antibiotics. Since you probably don't have the time or the resources to do this kind of scientific research, do some electronic research instead. Do a triage on your weeds. In this case what we mean by triage is find which weeds have information listed about the chemistry and/or biology of their seeds, stems and leaves. Discard all plants which have little or no recorded information and keep only those you find in your electronic research.
One approach to using garbage is to ask yourself why a perfectly good garbage plant is not being used now. For instance, if you live in a place that has lots of oak trees you may find yourself crunching across the acorns in the fall. Apparently the squirrels can only eat and store so many. The rest are left to be crushed and eventually rot under your feet. American Indians used acorns as food. Why don't we use them in this way? Let's suppose the acorns are bitter, or that their shells are too hard or that there are any number of problems with using them straight off the tree for food. What modern industrial process is there that would get rid of these problems and use the acorns for food?