This is a simplified explanation, however it should help explain why the cold sink is smaller than the heat sink:
A peltier cooler pumps heat from the cold side to the hot side, and in addition a peltier cooler generates heat in addition to the heat its pumping.
A peltier unit's Qmax (the amount of Watts it can pump) is rated at zero delta T (the difference in temperature between the cold and hot sides). Additionally, a peltier cooler's ability to pump heat diminishes as the delta T rises.
At some point (depending on the peltier unit design, etc.) the peltier will pump zero watts (btu) of heat when delta T rises too high.
So, to get the coldest temperatures possible on the cold side, you want to be able to remove as much heat as possible on the hot side. This needs to include any heat created by the peltier.
This coupled with the diminishing heat pumping ability when delta T rises, means that the cold sink is smaller than the heat sink, so the system has a high (or higher) coefficient of performance (COP) than a system with same size cold and hot heat sinks.
Hope this explains it.