In the medieval period, many (if not most) soldiers would have to equip themselves, sometimes but not always at their own expense. Although armories and stockpiles of war gear did exist, there wasn't enough to go around. No medieval power had the financial resources to outfit an army of ten or fifteen thousand men with heavy armor (much less all the other accouterments of war). Archers were drawn from the lower ranks of society, those who could not, for whatever reason, afford to equip themselves as heavily as the wealthier men-at-arms. So the causation of your question is somewhat backwards: archers did not have lighter armor because they were archers, they were archers because they could not afford heavier equipment.

However, this is not to say that archers were (as is often incorrectly asserted) "peasants" or particularly impoverished. Archers were quite often professional/semi-professional mercenaries and retainers or urban burghers/guildsmen serving in the civic militia. While neither of these groups were necessarily wealthy or socially elite, they were also not the poorest classes of society. This is especially true with the rise of contract armies in the 14th century: English archers of this period are quite often skilled tradesmen (tailors, armorers, etc.) or from military families, who might have equipped their eldest son as a man-at-arms but lacked the funds to pay for their second son or younger cousin to have the same expensive war gear. These archers were not necessarily as lightly equipped as movies would lead you to believe. Mail shirts, brigandines (in the 15th century), and padded coats (which were not as protective as plate, but still very functional) might all be worn by an archer, depending on his finances and luck. There is even one intriguing garrison record which indicates that "armored archers" were a distinct category, although what specifically this might refer to is unknown.