In the west up until the beginning of the last century the tradition was for confirmation and first communion to be celebrated at the same time, usually coinciding with the end of the child’s formal academic education and religious instruction. In industrial and agricultural areas this was generally about age 12-14 depending on local customs. The white dress or suit was actually a confirmation dress, and often the same as the child’s “graduation” dress, since in many or most places religious and academic instruction took place together in Catholic schools, or state schools run and taught by religious.
When Pope Pius X lowered the age of 1st communion to the age of reason, about 7, he did not address the age of confirmation, which usually remained the same as it had been, although in the middle of the century, at least in the US, it was often conferred anywhere between about 4th to 8th grade, where 8th grade marked graduation from Catholic school for working class children. As Catholic high schools and high school education for the majority became the norm, the age of confirmation was also pushed back, since the thinking remained that it was a sacrament of maturity and coming of age. Coincidentally, in many places robes for confirmation, similar to graduation robes, were commonly used, emphasizing the prevailing idea that confirmation marked “graduation” from formal religious instruction.
The various cultural accretions surrounding first communion are primarily ethnic and cultural in origin, rather than flowing from the theology of the sacrament: the white frilly dresses, veils, elaborate parties, gifts of money etc. The veil actually had its origin in the fact that when girls matured the assumed head coverings for modesty, and a scarf, shawl, mantle, bonnet, cap or similar head covering was the norm for both peasant, working class or upper class women. The variation in styles were based on custom and class but head coverings were universal until the 1920s or later for girls of marriageable age and women. So the communion veil coincided with the time the girl was becoming a young woman. When the age was lowerd, the veil was retained as part of the costume.