In a tricycle gear aircraft, the nosewheel supports little of the weight. The center of gravity of the aircraft is only slightly in front of the main gear, and so the nose gear only has to hold the small amount of weight required to keep the aircraft from tipping forward onto its nose.
Exactly how much weight the nosewheel has to support depends on how the aircraft is loaded. It is greatest when loaded to max gross weight, with the center of gravity at its most forward allowable.
As an example, a 1978 Cessna 152 has a max gross of 1670 pounds and a forward center of gravity limit at 32.65 inches* aft of the "datum," an imaginary plane passing through the front face of the firewall. The main wheels are located 47.1 inches aft of datum and the nose wheel is located 10.8 inches forward of datum.
Balancing out the forces and torques for this loading reveals that the main gear needs to support 1253 pounds and the nose gear supports only 417 pounds:
$ 417 + 1253 = 1670 $
$ 417(10.8)+1670(32.65)=1253(47.1) $
It tends to be even less for a tailwheel aircraft. Since the tailwheel is so far from the center of gravity, it has a long lever arm and very little force is required to produce a large torque.
*Note: at lighter weights, the center of gravity can be more forward than this, up to 31 inches aft of datum at 1350 pounds. At these loadings, the nose gear will support a higher percentage of the overall weight, but since the overall weight is smaller, the total weight supported by the nose gear is smaller. Example: at 1350 pounds with a center of gravity 31 inches aft of datum, the nose wheel supports 375 pounds. At 28% of the gross weight, this is a slightly larger percentage, but it is still a smaller number. It's possible that some aircraft's weight and balance requirements are such that the maximum loading on the nose gear is at some weight other than max gross.
