Marriage, in Fine

 Gender is an attribute of grammar, not sexuality.

Your sex is established at conception, and cannot be changed.
The word "marriage" appeared around 1300 and likely descended from the Old French "mariage" of the 12th Century and the Vulgar Latin "maritaticum" of the 11th Century, ultimately tracing to the Latin "maritatus", past participle of "maritare". Thus, the word "marriage" ultimately derives from Latin mātrimōnium, which combines the two concepts: mater meaning "mother" and the suffix -monium signifying "action, state, or condition."
Marriage referred to a right to inheritance. A man in the Roman Empire might have many concubines, sex slaves, prostitutes, etc., and might conceive children with all of them. However, only the offspring of the woman he married would have a right to inherit his estate. 

In short, to "marry" someone refers to the man's ability to make a woman into a mother, who bore children who could inherit. Thus, someone conceived and born as a woman cannot "marry" another woman, nor can someone conceived and born as a man "marry" another man.