The Romans had mail armor since about the 4th century BCE. It was called Lorica Hamata and was around well before the plate armor, Lorica Segmentata, which was introduced in about the 1st century CE and used until the fall of the Empire in the West. The use of segmentata supposedly came about because it was less tedious and time consuming to make.
There is also a story of Segmentata replacing mail because of the large number of mail shirts lost with the legions in the Tutenburg forest, but this is just speculation.
Roman mail was riveted, like the later medieval and early-modern variety, and was made from iron, as were their weapons.
Also the term chain mail is a neologism. Mail or the French word Maille is what scholars use today. The word Maille is derived from Macula in Latin, meaning mesh.
Riveted Mail doesn't have a huge weakness against thrusting weapons, especially when it is worn with a thick, foundation fabric underneath it. It's not as good as plate, but it does the job and requires a lot less skill to make.
This could be one of the reasons why it disappeared after the collapse of the Western Roman Empire in the 5th century CE.
Also, the weight of mail on the shoulders can easily be transfered in part to the waist by use of a belt, as was done in Roman and medieval times.