The way a wall is constructed obviously affects its thickness, but it also affects its weight. And the heavier a wall (and building) is, the more costly the foundations are likely to be to carry it.
Additionally, the form of construction affects the 'U'-value of the wall and thus the amount of energy needed to heat and cool the same building.
In a timber frame structure it is the timber frame that carries all the loads and provides support for any masonry or other cladding around the outside of the building. It is generally also the 'carrier' for whatever form of insulation is to be used.
Quite thin walls can carry buildings of 4 and more storeys. But they also limit the type of insulation that can be used to achieve the required 'U'-value and energy efficiency.