Over simplified here.
The mass (weight, volume) of the heatsink determines its thermal capacity.
The heatsink's surface area determines its heat-shedding rate.
Comparing two heatsinks, same surface area, but one twice the mass (or volume, weight):
The lighter heatsink will heat up faster,
But both heatsinks will shed heat at the same rate.
Comparing two heatsinks, same mass (or volume, weight), but one twice the surface area:
Both heatsinks will heat up at the same rate,
But, the smaller surface-area heatsink will eventually run hotter, the other cooler...