Get rid of your wheelbarrow.
Wheelbarrows are medieval, cumbersome, unwieldy, often heavy, monstrosities that should be banned from gardening circles and left to muscular, sweaty construction crews. Literally, although there is some evidence that the Greeks and Romans may have used something similar, the best evidence is that the wheelbarrow became popular during the dark Middle Ages of Western culture. As far as I am concerned it should have been left there in the Middle Ages.
I don't own a wheelbarrow anymore. I've had two in the past twenty years; a typical steel-bodied, one-wheel contraption, and a two-wheeled plastic cart. Both suffered from the same problems in my eyes; limited payload sizes, a strong tendency to tip over on uneven surfaces and with large loads, tiresome to drag back up the Flint Hills after emptying, and finally, they just took up too much storage space. I threw the last one out when it fell off its designated wall hanger and banged into my shin.
Instead, for the past five years, I've been happy using a simple flat bedsheet to collect all my spring garden debris. The particular bedsheet I use, pictured at right, is an old one, in fact it was a wedding gift for us 28 years ago, our first set of married sheets. Once retired from use for slumber and other indoor activities, it has been variously used over the years as a frost cover for plants, and as a dropcloth for painting walls and staining decks before it was requisitioned as a load-bearing device. In fact, it could still be used for most of those activities without sacrificing its usefulness as my substitute barrow. My "sheetbarrow." 
There are a number of advantages to a sheetbarrow, not the least of which is that you don't have to lift the load except to gather the forward three corners and angle them up a bit. In that regard, it still functions as a somewhat flexible Class II Lever (I'm sorry to introduce Physics 101 into the subject). The ground supports all the weight of the load and the energy to overcome the friction of a fairly smooth cotton surface against the smooth grass is substituted for the energy of bearing the weight of the load, to the benefit of my lumbar vertebrae. It stays where you stop, never trying to continue downhill in an accelerating fashion. It won't tip over a heavy load and smash your toes. It is light to carry back uphill after you dump the load and dumping the load is a simple matter of "flipping" the sheet. And it folds (or crumples) compactly for easy storage.
Now, it's true, you could purchase a reinforced plastic tarp or an expensive, heavy cansas tarp and accomplish the same task, but an old bedsheet is lighter, and doesn't make the irritating crackly plastic noises of a store-bought tarp. The stain and paint residue has left my bedsheet stiff in places and may have welded the fibers together to improve the material strength, but I've only got one small hole in it after five years of Spring use for all kinds of materials, including vast loads of thorny rose trimmings. And perhaps it is true that the sheetbarrow works exceptionally well in my circumstances because I garden on a hill and deposit all the wastes at the bottom of the hill so that I'm always moving the weight downhill over a smooth mown grass surface. But I can pile a lot of material, including limbs, on a bedsheet that I couldn't fit into a wheelbarrow and I've never had the bedsheet smash one of my toes.
So rummage through your closet, grab an old bedsheet, and give it a try. You may not agree that it performs quite as good as I've advertised, but I believe you'll find it an improvement over your typical hardware store wheelbarrow offering. If nothing else, the memories evoked by the old sheet may keep a smile on your face as you trudge down and back from the debris pile.
