Interestingly the spider silk of 5.4 GPa has higher tensile strength than the specimens of "pure" carbon nanotubes of 2cm measured in labs at 3.6 GPa. The theoretical limit of cabon nanotubes is said to be at 300 GPa, and it's assumed that materials with about 130 GPa of tensile strength would be needed for the "rope" of an space elevator.
According to wikipedia, the diameter of natural spider silk is 4µm, which is a cross section area of 1.26e-11 m². Multiplied by the tensile strength of natural spider silk (5.4 GPa) gives the capacity to lift 68 milinewtoms, or 7 Grams!