Lightweight furniture doesn't have to be modern. The old-fashioned armchairs in this photo from The Rug Company have graceful curves and turned legs that keep them from seeming bulky.
It also doesn't have to be uncomfortable. This Lenox Sofa from Room and Board looks like a good place to stretch out. Although it has lots of cushioning, the low arms and thin legs make it appear visually lightweight.
When shopping for a small space, look for something that fits the footprint of your apartment while leaving some breathing room. A few options are furniture with legs, streamlined upholstered items, clear glass and plastic pieces, wire furniture, wall-mounted storage units, and furniture with a reflective finish. Add your own suggestions for visually lightweight furniture in the comments below. Top and Bottom Photos: Knoll