The Linus shawl is one of those simple projects that works well in a variety of yarn weights. We've had a sample in our shop in the past, and for this summer, Liz worked up a new version with one skein of Brighton Beach, a sport-weight linen/cotton blend.
Knit at the upper end of the suggested needle size on a US5, it creates a drapey summer fabric that is perfect for taking the chill off a summer evening. It could easily be made larger by adding a second skein. The free pattern is available on Ravelry.