Is there any connection between minimum age for marriage in Catholic Church and tradition about Mary's age at Annunciation? According to Canonic law, the minimum age for marryage to be valid for girls is fourteen (it can be and usually is higher for the marriage not to be illicit):


  Can.  1083 §1. A man before he has completed his sixteenth year of age
  and a woman before she has completed her fourteenth year of age cannot
  enter into a valid marriage.


Since Mary gave birth to Jesus at similar age and is important enough to make an example of sort, I guess that tradition of her age at Annunciation may have played a role in forming of this law.

My question: is this role marginal, non-existent, or important? Are there any sources for it?
I do not think there is any connection in any Church document or scripture to the annunciation.

However, the sacraments have age requirements attached to them as a "rule of thumb."  A certain level of maturity and knowledge is required to receive a sacrament.  The Church could assign any age it deems necessary.  

Even though the ages are 14 and 16 according to Canon Law, I think you would be hard pressed to find a Deacon or Priest in the developed world who would marry a couple this young.