Which bird lays the smallest egg for its size?

The ostrich.

Although it is the largest single cell in nature, an ostrich egg is less than 1½ per cent of the weight
of the mother. A wren’s egg, by comparison, is 13 per cent of its weight.
The largest egg in comparison with the size of the bird is that of the Little Spotted kiwi. Its egg
accounts for 26 per cent of its own weight: the equivalent of a woman giving birth to a six-year-old
child.

An ostrich egg weighs as much as twenty-four hen’s eggs; to soft-boil one takes forty-five minutes.
Queen Victoria tucked into one for breakfast and declared it among the best meals she had ever eaten.

The largest egg laid by any animal – including the dinosaurs – belonged to the elephant bird of
Madagascar, which became extinct in 1700. It was ten times the size of an ostrich egg, nine litres in
volume and the equivalent of 180 chicken’s eggs.
The elephant bird (Aepyornis maximus) is thought to be the basis for the legend of the fierce roc
that Sinbad battles in the Arabian Nights.