The dimeric motor protein kinesin-1 moves processively along microtubules against forces of up to 7 pN. However, the mechanism of force generation is still debated. Here, we point to the crucial importance of diffusion of the tethered motor domain for the stepping of kinesin-1: small crowders stop the motor at a viscosity of 5 mPa·s-corresponding to a hydrodynamic load in the sub-fN (~10^{-4} pN) range-whereas large crowders have no impact even at viscosities above 100 mPa·s. This indicates that the scale-dependent, effective viscosity experienced by the tethered motor domain is a key factor determining kinesin's functionality. Our results emphasize the role of diffusion in the kinesin-1 stepping mechanism and the general importance of the viscosity scaling paradigm in nanomechanics.