In the Middle Ages, a bellwether was a sheep that wore a bell around its neck and led the flock around the countryside. Later, the word applied to any ringleader or person on the forefront of a profession or industry.
So, no: A robin is not a bellwether. But it is a harbinger. Robins flying north have always been a sign of spring's arrival. Cuckoos do the same in England.
Harbinger derives from the German word for "to lodge an army," and used to mean a shelter or encampment.
Later, the word meant a courier who'd go forth in advance to announce the arrival of an army or royal party and obtain lodging for them. From this came the meaning of "forerunner." That's how the robin and the cuckoo got into the act. And the crocus and the tree frog. But not the sheep. He's still a bellwether.
A nest egg, or the sum of money people put aside as savings, derives from the pottery or white glass eggs farmers used to place under a hen to induce the production of the real thing.
Reports show that farmers can increase hens' egg yield tenfold by leaving one of the eggs in the nest - or by putting in at least a good imitation.
From this custom came the figurative meaning of something laid aside for the future. Like a financial nest egg. Any money we put in the bank, like the porcelain egg, might encourage us to save or produce more.
This expression for someone past their prime comes from deceptive trade practices among poultry growers. Raising poultry has been going on since the beginning of civilization, and until recently, it was limited by seasons.
Years ago, growers had no way to incubate chicks in the winter, so customers had to wait for the summer markets. Sometimes, though, old birds from the year before were offered as part of the spring crop. Savvy customers knew that these tough fowl were "no spring chickens" and, after saying so enough times, they caused this tenderless expression to enter everyday usage.