Why would a mother allow her 16 year old daughter to get married?
It used to be very common for girls to marry right after high school, at a time when few girls went on to college. Most of the girls who did marry were 17-18 years of age and a few were even 16 years.
Girls and boys also married when it looked like the boy was going to be drafted into the military. Of course, in a time of war, married or not the boy had to go off to service.
The age of 16, today sounds a bit young to me. However, in the USA, some cultures approve of 16 year old girls being married, especially if they're expecting a baby.