What is the typical weight distribution ratio between nose gear and main gear?
Look at the sketch of the recommended gear placement relative to the center of gravity (cg) from this answer: 



We can calculate the load distribution for both extremes. For simplification we use the same angle of 60° for the nose wheel in both cases:


Main landing gear 6° aft of cg: $\frac{\tan 6°}{\tan 60°}$ = 6%
Main landing gear 20° aft of cg: $\frac{\tan 20°}{\tan 60°}$ = 21%


Add some dynamic loading from the application of wheel brakes. In this answer it is shown that the horizontal braking force is less than 30% of the maximum static weight of the aircraft, and applying this knowledge to the nose gear at 60° from the cg adds 0.3$\cdot\cos 60°$ = 15% of the maximum static load of a fully loaded aircraft to the nose gear load.

In extreme cases the nose gear would carry almost half of the aircraft mass, but then rotation would be impossible. In case of the Go-229 it was 45%.



Semi-finished Go-229 V3 (picture source)

On the other extreme you find nose gears with zero static load which were only intended for taking the braking forces.



Zeppelin Staaken R VI (picture source)