I worked on landing gear design in the past. The quick answer to why the nose whell, or more broadly the nose landing gear assembly, is "smaller" (than the MLG), is because it's as large as it needs to be and no more.
When the aircraft is statically on the ground, the NLG is designed to take about 5 to 15% of the total aircraft weight. The MLG as a whole takes 85 to 95% of the load, and for a typical tricycle with two MLG units, each unit then takes 42 to 47% of load, which is about 3 to 5 times as much as the NLG takes. This means that based on static loads, one can expect the NLG unit to be 3 to 5 times "weaker" than each MLG unit.
The image below shows a simple diagram for calculation of the load distribution between NLG and MLG:
There are a whole bunch of requirements on landing gear design, the static load distribution is only one of them.