Why is small-signal output resistance not dependant on device width
The small signal output resistance depends on W because \$I_D\$ depends on it. 

After all, you have:

$$R_o=\dfrac{1}{{\lambda}I_D} $$

With \$I_D\$ being the current in the saturation region for the MOSFET. In saturation, 
$$I_D=\dfrac{1}{2}\text{K}\frac{W}{L}(V_{GS}-V_T)^2$$ 

So yeah, if you increase W, the \$R_o\$ does decrease because \$I_D\$ is in its denominator.

$$R_o=\dfrac{1}{\dfrac{1}{2}{\lambda}\text{K}\frac{W}{L}(V_{GS}-V_T)^2} $$