According to the overall consensus of entries in Urban Dictionary, the term shorty is generally used in hip-hop music in reference to a woman, typically one desired by the speaker and, at times, a girlfriend. In songs from Billboard's year-end Top 10 charts (1951-2015), we find the use of the term to be largely restricted to songs of the first decade of the 21st century, as shown in the chart below: 

In fact, the term reaches its zenith, in terms of both total number of songs that includes and the total number of occurrences of it in these songs, in 2008. Among artists whose songs include variants of shorty are Kanye West (in 2006's "Gold Digger"), Akon (in 2007's "I Wanna Love You"), and Flo Rida (in 2008's "Low"); however, the artist in the collection most strongly associated with the term is Usher, as four of his songs include the term: "Yeah!" (2004), "Burn" (2004), "Love in this Club" (2008), and "OMG" (2010).

Interestingly, only two songs that include shorty in the collection are performed by female acts, and these constitute its earliest use in the collection (1999) and its most recent* (2014). Videos of these songs are provided below:

This analysis suggests that shorty is, at least with respect to the most popular music of the day, very much an artifact of the aughts and that its best days are behind it.

*It should be noted that it is not Katy Perry who uses shorty in "Dark Horse" but the rapper Juicy J, who uses it twice in his part of the song.