With little remaining energy, Mary hauled herself into elevator, fought the gravity generated by the ascent/ascension, and staggered out to the 14th floor.
Which word should I use? And why?
In your usage
With little remaining energy, Mary hauled herself into elevator, fought the gravity generated by the ascent, and staggered out to the 14th floor.
Since Mary is climbing upwards, her action is called an
ascent - (n) a climb or walk to the summit of a mountain or hill.
in mountaineering first attempts of climbing a mountain are called
It should be pointed out that your sentence does not really make sense since climbing upwards does not generate gravity.
Your other word has a very different meaning
ascension - (n) the act of rising to an important position or a higher level
June 2nd will be the 64th anniversary of Queen Elizabeth's ascension to the throne.
One of the most famous paintings of an ascension is Raphael's Transfiguration
This painting is also the subject of one of the largest "instant" Poloroids ever
Ascent and ascension are similar words, certainly, but the meaning is not the same:
ascent (n) : the act of rising or mounting upward, an advance in social status or reputation
ascension (n): the act of rising or ascending; especially : the act of moving to a higher or more powerful position
In your example it would be better to use ascent since that conveys only that Mary is moving upwards. Meanwhile, ascension, without any further context, implies that she is ascending toward Heaven, since that is a context in which the word is commonly used.