35mm vs. 50mm & 50mm vs. 85mm

[Daniel Browning]

If you need to stop this lens down to f/4 to get good sharpness

By f/2.8 the 50mm f/1.4 it's noticeably sharper than the 24-70.

than what are it's advantages over my 24-70 f/2.8 besides size and weight?

For me, the primary advantages are control over DOF and low light photography, either of which can be more important than sharpness. There can be other benefits as well, such as less distortion, vignetting, bokeh, flare, etc. (In the case of this lens, however, few of those apply.) This has to be weighed against the flexibility of zooming of course. Generally, I tend to use the 50mm f/1.4 wide open when the subject has low contrast (low dynamic range), such as in studio flash setups. If the scene has a lot of dynamic range (high contrast), I'll stop down to f/2.8 because I dislike the flare/halation.