Not all Asians have “smaller” eyes. This mainly applies to East Asians. Their eyes aren’t technically smaller, either. They simply have an extra patch of skin called an epithelial fold above their eyes.
That fold allows them to protect their eyes against extreme cold and fierce winds that occur in Tibet. Average annual snowfall is 18 inches and the land is severely dry 9 months out of the year.
The epithelial fold is simply the way they adapted to their environment. Tibet is where the ancestors of many East Asians lived for tens of thousands of years before migrating to warmer places. The epithelial fold, however, is part of the DNA now and so continues to be a trademark of East Asians.